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INTELLIGENT MATERIAL HANDLING MOBILE ROBOT FOR
INDUSTRIAL PURPOSE WITH ACTIVE FORCE CONTROL CAPABILITY
(ROBOT MUDAH GERAK PENGENDALI BAHAN PINTAR UNTUK
KEGUNAAN INDUSTRI DENGAN KEUPAYAAN KAWALAN DAYA
AKTIF)
MUSA BIN MAILAH
HISHAMUDDIN JAMALUDDIN
ENDRA PITOWARNO
DIDIK SETYO PURNOMO
TANG HOWE HING
MOHAMAD AKMAL BAHRAIN ABDUL RAHIM
RESEARCH VOTE NO: 74016
PUSAT PENGURUSAN PENYELIDIKAN UNIVERSITI TEKNOLOGI MALAYSIA
2007
UNIVERSITI TEKNOLOGI MALAYSIA
UTM/RMC/F/0024 (1998)
BORANG PENGESAHAN
LAPORAN AKHIR PENYELIDIKAN
TAJUK PROJEK : INTELLIGENT MATERIAL HANDLING MOBILE ROBOT FOR
INDUSTRIAL PURPOSE WITH ACTIVE FORCE CONTROL
CAPABILITY
Saya _________________________MUSA BIN MAILAH_ ___________________________ (HURUF BESAR)
Mengaku membenarkan Laporan Akhir Penyelidikan ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut :
1. Laporan Akhir Penyelidikan ini adalah hakmilik Universiti Teknologi Malaysia.
2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan rujukan sahaja.
3. Perpustakaan dibenarkan membuat penjualan salinan Laporan Akhir
Penyelidikan ini bagi kategori TIDAK TERHAD.
4. * Sila tandakan ( / )
SULIT (Mengandungi maklumat yang berdarjah keselamatan atau Kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972). TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh Organisasi/badan di mana penyelidikan dijalankan). TIDAK TERHAD
TANDATANGAN KETUA PENYELIDIK
PROFESOR MADYA DR. MUSA MAILAH Nama & Cop Ketua Penyelidik Tarikh : 10 APRIL 2007
/
CATATAN : * Jika Laporan Akhir Penyelidikan ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi berkenaan dengan menyatakan sekali sebab dan tempoh laporan ini perlu dikelaskan sebagai SULIT dan TERHAD.
Lampiran 20
iii
DEDICATION
To ALL Intelligent Active Force Control
(IAFC) group members –
a BIG thank you for your contributions …
iv
ACKNOWLEDGEMENTS
We would like to express our sincere gratitude and appreciation to the
Ministry of Science Technology and Innovation (MOSTI), Malaysia, for providing
the project research grant (Project No.: 03-02-06-0038EA067) and the Universiti
Teknologi Malaysia (UTM) for their full support in terms of accommodating the
research infrastructures and facilities. Special thanks go to Dr. Mohamad Kasim
Abdul Jalil from the Department of Design, Abdul Rahim Mohamad, Ahmad Faisal
and Ahmad Shahrizam from the Industrial Automation Laboratory for their
meaningful contribution in assisting some of the works related to this project. Last
but not least to everyone who has in one way or another contributed to the success of
this project.
v
v
ABSTRACT
This report presents both theoretical and experimental studies of a wheeled mobile
system that incorporates a number of intelligent and robust closed-loop control schemes. The
system may actually represent an automated material-handling transporter that can be effectively
used in a manufacturing or industrial environment. An integrated kinematic and dynamic control
with embedded intelligent algorithms were the main approaches employed for the robust motion
control of a mobile manipulator (MM) comprising a differentially driven wheeled mobile base
platform with a two-link planar arm mounted on top of the platform. The study emphasizes on
the integrated kinematic and dynamic control strategy of the schemes in which the former
serving as the outer most control loop is used to manipulate the trajectory components while the
latter constituting the inner active force control (AFC) loop is implemented to compensate the
dynamic effects including the bounded known or unknown disturbances and uncertainties while
the system is executing trajectory tracking tasks. The proposed intelligent schemes considered in
the study are the fuzzy logic (FL) and knowledge-based system (KBS) strategies that are
incorporated into the AFC schemes to automatically estimate the inertia matrix of the system
necessary to trigger the disturbance rejection capability. A virtual mobile system was also
designed and included in the study to demonstrate the system capability to operate effectively in
a virtual computer integrated manufacturing (CIM) environment. The effectiveness and
robustness of the proposed schemes were investigated through a rigorous simulation study and
later complemented with experimental results obtained through a number of experiments
performed on a fully developed working prototype in a laboratory setting. A number of
disturbances in the form of vibratory and impact forces are deliberately introduced into the
system to evaluate the system performances. The investigation clearly demonstrates the excellent
robustness feature of the proposed control scheme compared to other systems considered in the
study.
vi
ABSTRAK
Laporan ini mengetengahkan kajian teori dan praktik suatu sistem mudah gerak beroda
yang melibatkan beberapa skema pintar dan kawalan gelung tertutup. Sistem ini sebenarnya
boleh mewakili suatu pengangkut untuk pemindahan bahan automatik yang boleh digunakan
secara berkesan di dalam persekitaran pembuatan atau industri. Kesepaduan kawalan kinematik
dan dinamik serta penggunaan algoritma kawalan merupakan pendekatan utama yang digunakan
untuk mengawal dengan lasak pergerakan Pengolah mudah gerak (MM) yang terdiri daripada
pemacuan differential pelantar mudah gerak beroda dengan lengan dua-penyambung dipasang di
atas pelantar tersebut. Kajian memberi penekanan terhadap strategi kesepaduan skema kawalan
kinematik dan dinamik di mana bahagian pertama yang wujud di bahagian luar gelung kawalan
digunakan untuk mengolah komponen trajektori manakala bahagian kedua melibatkan gelung
dalaman kawalan daya aktif (AFC) berrtindak sebagai pemampas kesan dinamik termasuk
gangguan terhad diketahui atau tidak dan juga ketidaktentuan semasa sistem beroperasi dalam
melaksanakan tugas penjejakan trajektori. Skema pintar yang dicadangkan dalam kajian adalah
strategi kawalan logic kabur (FL) dan system berasaskan-pengetahuan (KBS) yang dimuatkan ke
dalam AFC untuk menganggarkan matriks inersia sistem secara automatik yang diperlukan
untuk menggerakkan keupayaan sistem menghapus gangguan. Suatu sistem mudah gerak maya
juga direka bentuk and dimuatkan di dalam kajian untuk mempamerkan kebolehan sistem
beroperasi dengan berkesan di dalam persekitaran maya pembuatan komputer bersepadu (CIM).
Keberkesanan dan kelasakan skema yang dicadangkan diselidiki menerusi kajian simulasi dan
kemudiannya dilengkapi dengan keputusan eksperimen yang diperolehi melalui beberapa
eksperimen yang dijalankan terhadap prototaip di dalam persekitaran makmal. Beberapa bentuk
gangguan getaran dan hentakan dikenakan pada sistem untuk menilai prestasi system tersebut.
Keputusan penyelidikan menunjukkan dengan jelas keupayaan lasak yang baik ditunjukkan oleh
skema sistem kawalan cadangan berbanding dengan skema lain yang dipertimbangkan dalam
kajian.
.
vii
CONTENTS
CHAPTER SUBJECTS PAGE
TITLE PAGE i
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
CONTENTS vii
LIST OF TABLES xiii
LIST OF FIGURES xiv
LIST OF SYMBOLS/ABBREVIATIONS xix
LIST OF APPENDICES xxiv
CHAPTER 1 INTRODUCTION 1
1.1 General Introduction
1.2 Outline of Research
1.3 Objective of Research
1.4 Scope of Research
1.5 Research Methodology
1.6 Organization of Report
CHAPTER 2 THEORETICAL FRAMEWORKS AND 10
REVIEW
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viii
2.1 Introduction
2.2 Mathematical Modelling of Mobile Manipulator
2.2.1 Dynamics of Mobile Manipulator
2.2.2 Kinematics of Mobile Manipulator
2.2.3 Dynamics of Mobile Platform
2.2.4 Dynamics of Manipulator Arm
2.2.5 Kinematic Control of Mobile Manipulator
2.2.6 Dynamic Control of Mobile Manipulator
2.3 Resolved Motion Rate Control and Resolved
Acceleration Control
2.4 Active Force Control (AFC)
2.4.1 Estimated Inertia Matrix
2.4.2 Estimation of Inertia Matrix using Intelligent
Schemes
2.5 Knowledge Based System
2.6 Fuzzy Logic
2.7 Knowledge Based Fuzzy Control
2.7.1 Knowledge Based Reasoning in Fuzzy System
2.8 Motion Planning
2.8.1 Path Planning
2.8.2 Trajectory Planning
2.9 Virtual Reality (VR)
2.10 Conclusion
CHAPTER 3 ESTIMATION OF INERTIA MATRIX BASED 48
ON ωv -ACTIVE FORCE CONTROL WITH
FUZZY LOGIC
3.1 Introduction
3.2 Fuzzy Logic Applied to Robotics
3.3 Fuzzy Logic Design
3.3.1 Definition of the Linguistic Variables
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ix
3.3.2 Determination of Fuzzy Set
3.3.3 Design of the Fuzzy Rules
3.4 Simulation
3.5 Results and Discussion
3.6 Conclusion
CHAPTER 4 VIRTUAL WHEELED MOBILE ROBOT 60
SIMULATOR
4.1 Introduction
4.2 Robot Simulator
4.3 Overall Architecture of Virtual WMR
Simulator
4.4 Trajectory Planning
4.5 Scene Graph of Virtual Environment
4.6 Simulation Setup
4.7 Simulation Results and Discussion
4.8 Conclusion
CHAPTER 5 RESOLVED ACCELERATION CONTROL 77
AND ACTIVE FORCE CONTROL (RACAFC)
OF MOBILE MANIPULATOR
5.1 Introduction
5.2 Proposed MM-RACAFC Scheme
5.3 Proposed RACAFC for Mobile
Platform Section
5.4 Simulation
5.4.1 Simulation Parameters
5.4.2 Simulink Block Diagrams
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5.5 Results and Discussion
5.5.1 RACAFC for DDMR
5.5.2 Mobile Manipulator Control
5.5.2.1 Simulation Procedure
5.5.2.2 The optimum Kp, Kd
and IN obtained
5.5.2.3 Effect of Constant Torque
5.5.2.4 Effect of Impact Disturbance
5.5.2.5 Effect of Vibration
5.6 Conclusion
CHAPTER 6 RESOLVED ACCELERATION CONTROL 111
AND KNOWLEDGE-BASED FUZZY
ACTIVE FORCE CONTROL (RACKBAFC)
OF MOBILE MANIPULATOR
6.1 Introduction
6.2 Proposed MM-RACKBFAFC Scheme
6.2.1 RAC Section
6.2.2 KBFAFC Section
6.2.3 Knowledge Investigation and
Representation
6.2.4 Knowledge Acquisition and
Processing
6.2.5 KBF Design
6.3 Simulation
6.4 Results and Discussion
6.4.1 Effects of Constant Torque
Disturbance
6.4.2 Effects of Impact
Disturbance
6.4.3 Effects of Vibration
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xi
6.5 Conclusion
CHAPTER 7 EXPERIMENTAL MOBILE MANIPULATOR 134
7.1 Introduction
7.2 Specifications of Mobile Manipulator
7.3 Personal Computer (PC) Based
Controller
7.3.1 Computer and Data Acquisition
System Card
7.3.2 Frequency to Voltage Converter
(f/V) Circuits
7.3.3 Rotary Encoder Circuits using
HCTL2000
7.3.4 Signal Conditioning Interfaces
7.3.5 Programming Design
7.4 Embedded Controller using PIC16F877
7.4.1 Embedded Controller Circuit
7.4.2 Controller Card
7.4.3 Experimental Results and
Discussion
7.5 Conclusion
CHAPTER 8 CONCLUSION AND RECOMMENDATIONS 155
8.1 Conclusion
8.2 Recommendations for Future Works
REFERENCES 158
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xii
APPENDICES
Appendix A: Notes on Heuristic Search Algorithms 165
Appendix B: Computer Program for the Development of
Virtual Environment (VE) 168
Appendix C: Program Modules for the Experimental Mobile
Manipulator 175
Appendix D: List of Publications 182
Appendix E: Achievements / Outputs / Beneficiaries / Awards 185
Appendix F: Mechanical Design and Production Drawings of
Mobile Manipulator 188
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xiv
LIST OF FIGURES
FIGURE. NO TITLE PAGE
2.1 (a) A mobile platform and (b) A mobile manipulator 15
2.2 A schematic diagram of RMRC 27
2.3 An illustration of the RMAC/RAC schematic diagram 28
2.4 Typical AFC loop 29
2.5 RAC combined with AFC 30
2.6 An illustration of a generic expert system 34
2.7 An illustration of KBS 35
2.8 An illustration of a fuzzy logic system 37
3.1 Inputs and outputs of the fuzzy controller 50
3.2 Comparison of trajectory tracking error using various inputs 51
3.3 Inputs functions 52
3.4 Estimated inertia matrix as the output function 53
3.5 Fuzzy rules 54
3.6 Extended estimated inertia matrix 54
3.7 Rule editor and surface viewer 55
3.8 Rules viewer 56
3.9 Simulink block diagram of ωv -AFC-FL 56
3.10 Comparison of the trajectory tracking errors in
various disturbances 57
3.11 Comparison of the trajectory tracking error
between ωv -AFC and ωv -AFC-Fuzzy 58
4.1 Interlinking of motion planning, motion control and VR 62
4.2 A block diagram of the virtual WMR simulator 63
xv
4.3 Hierarchical structure of the scene graph for a VE 67
4.4 Procedures of VE rendering for a hierarchical structured
scene graph 69
4.5 Performance of the simulator under various loading conditions 74
4.6 Several views of the constructed virtual WMR simulator 75
5.1 Outline of the proposed MM-RACAFC scheme 78
5.2 The proposed MM-RACAFC scheme 79
5.3 The MM-RAC scheme 79
5.4 The RAC controller 80
5.5 The proposed AFC controller 80
5.6 Schematic diagram of the proposed MM-RACAFC 82
5.7 The proposed AFC applied to the DDMR 86
5.8 DDMR Trajectory 88
5.9 MM Trajectory 88
5.10 Impact Signals 89
5.11 Vibration Signals 89
5.12 Simulink diagram of DDMR-RACAFC 90
5.13 Simulink diagram of MM-RAC 91
5.14 Simulink diagram of MM-RACAFC 91
5.15 Simulink diagram of the input functions for MM simulation 92
5.16 Simulink diagram of the Mobile Platform Input Function 92
5.17 Simulink diagram of the Tip Position Input Function 93
5.18 Simulink diagram of the RAC Controller plus
Inverse Kinematics section 93
5.19 Simulink diagram of Inverse Kinematics of the manipulator 94
5.20 Simulink diagram of Inverse Kinematics of mobile platform 94
5.21 Simulink diagram of Direct Kinematics of MM 95
5.22 Simulink diagram of Direct Kinematics of manipulator 95
5.23 Simulink diagram of Direct Kinematics of mobile platform 95
5.24 Simulink diagram of Performance Display section 96
5.25 Simulink diagram of Inverse Dynamics of MM 96
5.26 Simulink diagram of the constraint matrix M(q) 97
5.27 Simulink diagram of the manipulator’s dynamics 97
5.28 Results of IN tuning (the white bar indicates
xvi
the optimum value) 99
5.29 (a) TTE with no disturbances 99
5.29 (b) TTE with disturbances 99
5.30 (a) Robot Animation for the RAC 100
5.30 (b) Robot Animation for the RACAFC 100
5.31 A flow chart showing the simulation procedures 101
5.32 (a) TTE of Arm for MM-RAC at Qc 104
5.32 (b) TTE of Arm for MM-RACAFC at Qc 104
5.33 (a) TTE of Body for MM-RAC at Qc 105
5.33 (b) TTE of Body for MM-RACAFC at Qc 105
5.34 The dialog box for External Disturbance Section 106
5.35 (a) TTE of Arm for MM-RAC at Qimp 107
5.35 (b) TTE of Arm for MM-RACAFC at Qimp 107
5.36 (a) TTE of Body for RAC at Qimp 108
5.36 (b) TTE of Body for RACAFC at Qimp 108
5.37 (a) TTE of Arm for MM-RAC at Qvib 109
5.37 (b) TTE of Arm for MM-RACAFC at Qvib 109
5.37 (c) TTE of Body for MM-RAC at Qvib 109
5.37 (d) TTE of Body for MM-RACAFC at Qvib 109
6.1 The proposed MM-RACKBFAFC 112
6.2 An illustration of global knowledge of mobile manipulators 115
6.3 The selected semantic networks of the MM’s knowledge
structure 115
6.4 The qualitative investigation in a semantic network 116
6.5 (a) The trajectory tracking of the mobile manipulator 117
6.5 (b) The track error at the tip end position for five cycles
of repeating tasks in the simulation 118
6.5 (c) The track error at the tip end position for four cycles
of repeating tasks in the simulation 118
6.6 (a) Angular velocity versus track error at joint-1 119
6.6 (b) Angular velocity versus track error at joint-2 119
6.6 (c) Angular velocity versus track error at wheel-L 119
6.6 (d) Angular velocity versus track error at wheel-R 119
6.7 (a) Inference input signal of KBF for manipulator 122
xvii
6.7 (b) Inference input signal of KBF for manipulator 122
6.7 (c) Inference input signal of KBF for mobile platform 122
6.7 (d) Inference input signal of KBF for mobile platform 122
6.8 (a) MFs of input of joint-1 and joint-2 124
6.8 (b) MFs of output of joint-1 and joint-2 124
6.8 (c) MFs of input of wheel-L and wheel-R 124
6.8 (d) MFs of output of wheel-L and wheel-R 124
6.9 Simulink diagram of the proposed MM-RACKBFAFC 125
6.10 (a) Simulink diagram of the block of KBFAFC 126
6.10 (b) Simulink diagram of the block of KBF System 126
6.11 (a) TTE of Arm, AFCKBFAFC, Qc= [0.2;0.2;0.5;-0.5] Nm 128
6.11 (b) TTE of Arm, AFCKBFAFC, Qc= [2;2;5;-5] Nm 128
6.11 (c) TTE of Arm, AFCKBFAFC, Qc= [20;20;20;-20] Nm 128
6.11 (d) TTE of Arm, AFCKBFAFC, Qc= [30;30;30;-30] Nm 128
6.12 (a) TTE of Arm, AFCKBFAFC, Qimp, Qgain = 0.1 129
6.12 (b) TTE of Arm, AFCKBFAFC, Qimp, Qgain = 0.5 129
6.12 (c) TTE of Arm, AFCKBFAFC, Qimp, Qgain = 1 129
6.12 (d) TTE of Arm, AFCKBFAFC, Qimp, Qgain = 3 129
6.13 (a) TTE of Body, AFCKBFAFC, Qimp, Qgain = 0.1 130
6.13 (b) TTE of Body, AFCKBFAFC, Qimp, Qgain = 0.5 130
6.13 (c) TTE of Body, AFCKBFAFC, Qimp, Qgain = 1 130
6.13 (d) TTE of Body, AFCKBFAFC, Qimp, Qgain = 3 130
6.14 (a) TTE of Arm, AFCKBFAFC, Qvib, Qgain = 0.1 131
6.14 (b) TTE of Arm, AFCKBFAFC, Qvib, Qgain = 0.5 131
6.14 (c) TTE of Arm, AFCKBFAFC, Qvib, Qgain = 1 131
6.14 (d) TTE of Arm, AFCKBFAFC, Qvib, Qgain = 3 131
6.13 (a) TTE of Body, AFCKBFAFC, Qvib, Qgain = 0.1 132
6.13 (b) TTE of Body, AFCKBFAFC, Qvib, Qgain = 0.5 132
6.13 (c) TTE of Body, AFCKBFAFC, Qvib, Qgain = 1 132
6.13 (d) TTE of Body, AFCKBFAFC, Qvib, Qgain = 3 132
7.1 (a) Isometric view of the mobile manipulator 137
7.1 (b) A photograph of the mobile manipulator in action 137
7.1 (c) Proposed gripper attached to the manipulator 137
7.2 An experimental set-up for the PC-based controller 138
xviii
7.3 Schematic diagram of the PC based controller 138
7.4 Two units of DAS1602 cards on the CPU Board 140
7.5 Frequency to Voltage Converter circuit 141
7.6 HCTL2000 based Rotary Encoder Signal Conditioner 142
7.7 Signal conditioning interface for the mobile platform 143
7.8 Signal conditioning interface for the manipulator 144
7.9 Display window of the calibration process through
the program MMH852.EXE 145
7.10 A sample of the display captured from the PC screen 146
7.11 A descriptive diagram of the autonomous mobile manipulator 146
7.12 Pins configuration of PIC16F8771 147
7.13 Circuit diagram of PIC16F877 based controller 149
7.14 (a) A view of the Autonomous Mobile Manipulator 150
7.14 (b) The mounting of the embedded controller 150
7.14 (c) The PIC 16F877 based embedded controller 150
7.14 (d) Power Supply unit for the embedded controller 150
7.15 Experimental results of the RACAFC scheme 151
7.16 Experimental results of the RACKBFAFC scheme 152
7.17 Tracking error of the arm in the experiment
of RACAFC and RACKBFAFC schemes 152
7.18 Actual acceleration at the joints, RACAFC and RACKBFAFC 153
7.19 Actual motor currents at the joints, RACAFC
and RACKBFAFC 153
xiii
LIST OF TABLES
TABLE. NO TITLE PAGE
3.1 Acceleration 51
3.2 Linear velocity 51
3.3 Estimated inertia matrix, IN 52
5.1 Specifications of mobile manipulator 87
5.2 The prescribed trajectories 88
5.3 The disturbances 88
5.4 Properties of impact and vibration disturbances 89
5.5 Simulation methods and parameters 90
6.1 The knowledge representation 120
6.2 The inference mechanism 121
7.1 Specification of the rig 136
xix
LIST OF SYMBOLS
SYMBOL
SUBJECT
)(qA
)(qB
b
),( qqC &
d
),( qqF &
g
G(s)
Gc(s)
H(s)
h
I
I′
Im
mI ′
Ic
IN, IN
INF
INI
INIF
Constraint matrix
Input transformation matrix
Half width of the robot
Centripetal and Coriolis matrix
the distance of point G to F of mobile manipulator
Friction and gravitational vector
Acceleration due to gravity (m/s2)
A function in La place domain representing the
feedforward gain in the AFC loop
A function in La place domain representing the
controller gain
A function in Laplace domain representing the
compensated gain in the AFC loop
Vector of the Coriolis and centrifugal torques
Inertia
Estimated inertia
Motor current
Measured motor current Applied motor current
Estimated Inertia matrix
Fixed IN
Integral IN
Fixed integral IN
xx
INinit
INIV
INKBF
INP
INPF
INPV
INRACAFC
J
Kp
Kd
KpRACAFC
KdRACAFC
Ktn rℜ∈λ
M(q)
m
Q
Q′
Q*
Qc
Qca
Qcb
Qcc
Qcd
Qgain
Qimp
Qvib
pq ℜ∈
r
)(qS
θ
θ&
Initial IN
Varied integral IN
Knowledge-based fuzzy IN
Proportional IN
Fixed proportional IN
Varied proportional IN
Fixed (crude) IN of RACAFC scheme
Jacobian
Proportional constant
Derivative constant
Proportional constant for RACAFC scheme
Derivative constant for RACAFC scheme
Motor torque constant
Lagrange multiplier
Symmetric and positive definite inertia matrix
Mass
Bounded (known/unknown) disturbance
Measured disturbance
Estimated disturbance
Constant torque disturbance
Qc of [0.2 0.2 0.5 -0.5]T Nm
Qc of [2 2 5 -5]T Nm
Qc of [20 20 20 -20]T Nm
Qc of [30 30 30 -30]T Nm
Scaling factor for impact and vibration
Impact disturbance
Vibration disturbance
p generalized coordinate
radius of wheel
Transformation matrix
Angular position
Angular velocity
xxi
θ&&
θ&&
refθ
refθ&
refθ&&
actθ
actθ&
actθ&&
Tq
φ
Angular acceleration
Measured angular acceleration
Reference angular position
Reference angular velocity
Reference angular acceleration
Actual angular position
Actual angular velocity
Actual angular acceleration Torque
Applied torque
Heading angle of platform
xxii
LIST OF ABBREVIATIONS
ADC
AFC
AGV
AI
CIM
CPU
D
DAC
DAS
DC
DDMR
DOF
DOS
FL
FS
I
IL
ILC
KBF
KBFAFC
KBS
MF
MM
MMAFCON
NN
P
Analog to Digital Converter
Active Force Control
Automated Guided Vehicle
Artificial Intelligence
Computer Integrated Manufacturing
Central Processing Unit
Derivative
Digital to Analog Converter
Data Acquisition System
Direct Current
Differentially Driven Mobile Robot
Degree of Freedom
Disk Operating System
Fuzzy Logic
Fuzzy System
Integral
Iterative Learning
Iterative Learning Control
Knowledge Based Fuzzy
Knowledge Based Fuzzy Active Force Control
Knowledge Based System
Membership Function
Mobile Manipulator
Mobile Manipulator Active Force Control Online
Neural Network
Proportional
xxiii
PC
PD
PI
PIC
PID
PLC
RAC
RACAFC
RACKBFAFC
RMAC
RMRC
RTM
RTW
SMI
TTE
VE
VR
WMR
WTK
Personal Computer
Proportional plus Derivative
Proportional plus Integral
Peripheral Interface Controller
Proportional plus Integral plus Derivative
Programmable Logic Controller
Resolved Acceleration Control
Resolved Acceleration Control - Active Force Control
Resolved Acceleration Control - Knowledge Based Fuzzy
Active Force Control
Resolved Motion Acceleration Control
Resolved Motion Rate Control
Real-Time Monitor
Real-Time Workshop
Small and Medium-sized Industries
Trajectory Tracking Error
Virtual Environment
Virtual Reality
Wheeled Mobile Robot
WorldToolKit
xxiv
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Notes on Heuristic Search Algorithms 165
B Computer Program for the Development of
Virtual Environment (VE) 168
C Program Modules for the Experimental Mobile Manipulator 175
D List of Publications 182
E Achievements / Outputs / Beneficiaries / Awards 185
F Mechanical Design and Production Drawings of Mobile
Manipulator 188
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CHAPTER 1
INTRODUCTION
1.1 General Introduction
The mobile manipulator is basically a conventional robotic arm mounted on a
moving base. It is analogous to a human being considering the body and arm
sections. He or she must control these parts integrally when performing a dynamic
task to achieve the desired performance. As an example a welder carrying out a
welding operation needs to carry out the task by coordinating (control)
simultaneously and continuously both the arm and body movements so that a
favorable outcome could be obtained from executing the task. It is indeed more
challenging when the human operators are replaced by robots or automated
machines. It is desirable that the system is equipped with intelligence and robust
control capability so that it can perform its tasks satisfactorily and according to
specific requirements. Thus, it has to be designed and developed taking into account
the aforesaid criteria. Subsequently, comprehensive analytical studies on the
kinematics, dynamics and control aspects of the physical system should be carefully
carried out in order to come up with an alternative system that produces results
comparable to those of human operators. It is useful to note that the mobile
transporter described throughout this report shall be synonymously known as
wheeled mobile robot (WMR) or mobile manipulator.
2
1.2 Outline of Research
The use of an autonomous mobile robot as a material handling robot
(transporter) is common in the manufacturing and industrial sector including the
Small and Medium-sized Industries (SMI). This implementation of such a system is a
well known fact in view of its ability to replace the operator’s (human) inconsistency
and shortcoming for repetitive, labour intensive, arduous and continuous tasks. The
mobile robot used in this context is usually known as Automated Guided Vehicle
(AGV). The AGV system has however severe limitations in terms of intelligence (in
decision making) while navigating and usually prone to errors whenever it is subject
to obstacles or disturbances in its path. In addition to that industrial AGV normally
transports passively the work piece or material within the plant layout on the shop
floor. This project involves the design and development of a new, innovative,
intelligent and robust mobile robot as a transporter with the incorporation of a novel
control scheme employing Active Force Control (AFC) strategy. A very useful
feature of the proposed system is the presence of a dexterous robotic arm that can
manipulate positively (via gripper) parts or materials to be transported. It is expected
that in the process of manipulating work pieces or parts dynamically by maneuvering
the system along a specific guided path, the transporter is subject to a number of so
called ‘disturbances and uncertainties’. These may be in the form of obstacles in its
path, different payloads, complexity of the shape of the parts, compliancy with the
environment, vibration of the system, unexpected loading condition, friction (internal
or external) and others. The practical AFC scheme has been shown to demonstrate
superior robust and effective all round performance in encountering and
compensating the disturbances and uncertainties prevalent in dynamical systems. At
the same time, intelligent mechanism shall be incorporated into the system to make
appropriate decisions when the robot encounters a number of conditions while
performing its task. It is the aim of the project to come up with a practical mobile
robotic system with real-time active force control scheme which has the quality and
capability of handling and transporting the materials robustly, smoothly and
efficiently. Sensory devices are appropriately installed at strategic location on the
system to provide the essential feedback mechanism. Besides, a vision system is also
used to enhance the intelligence of the system. A total mechatronic approach is
3
applied in the design and development of the system involving the practical
integration of mechanical, electrical/electronic and computer control.
1.3 Objective of Research
The specific objective of research is to design and develop fully a working
prototype of an intelligent and autonomous material handling mobile robot (WMR or
mobile manipulator) for use in an SMI environment.
1.4 Scope of Research
The scope of research shall encompass the followings:
• Literature review on mobile manipulator modelling, motion control and
intelligent systems applied to robot control.
• The mobile robot is of a differentially driven wheeled type. Motion and path
planning of the mobile robot shall be investigated and applied considering only
nonholonomic constraints.
• Theoretical design and simulation of a number of advanced robust motion
control schemes based on Active Force Control (AFC) with intelligent
elements, namely fuzzy logic (FL) and knowledge-based system (KBS). The
application of a virtual reality technique shall also be explored in the research.
The main software design tool is MATLAB/Simulink.
• Design and development of an experimental mobile manipulator including
mechatronics design of the robot, PC-based interfacing, sensors and actuators
interfacing and a robot controller programming using C language. A hardware-
4
in-the-loop system based on MATLAB/Simulink and Real-Time Workshop
(RTW) shall be rigorously experimented. The possibility of using a
microcontroller (wireless and embedded system) and digital camera as a vision
system shall also be explored. The testing will be done in a laboratory setting
that emulates a factory layout.
1.5 Research Methodology
The project will be divided into five main parts. These are modelling and
simulation using computer, intelligent controller design, design and development
of the prototype, experimentation and performance evaluation and analysis.
Initially these areas will be investigated separately by groups of researchers under
the supervision of a project leader. Ideas and findings by all the groups will be
presented to other group members for transfer of knowledge and experience. The
more detailed description of the research methodology is as follows:
i. Computer modelling and simulation
The modelling and simulation phase involves rigorous study of mathematical
equations representing the system’s kinematics and dynamics. The modelling will
take into account realistic and valid assumptions related to the physical systems such
as the manipulator and steering or navigation mechanism. Classical control plus
intelligent techniques using FL and KBS will be studied independently and later
implemented with the AFC strategy to control the system. Their algorithms and
techniques will be thoroughly investigated and studied. Comprehensive simulation
works will include the evaluation of the system’s performance and robustness against
various forms of disturbances and other different operating conditions. Changes in
the parameters such as those related to the physical arm, simulation and learning
algorithms will also be also taken into account. Comparative study between the
control strategies will also be considered to provide a useful platform in determining
the optimum control method. The simulation works serve as a basis for designing
and developing the prototype in later stages.
5
ii. Intelligent controller design
A suitable intelligent controller will be identified based on the outcome of the
simulation study. The controller is chosen such that its practical implementation in
real time is feasible and readily applied. Relevant parameters of the controller will be
refined and related computer program will be written for this purpose. Development
of a possible hardware for the controller will be investigated and looked into. This
will largely involve aspects of computer programming, interfacing,
electrical/electronics and embedded system technology.
iii. Design and development of the prototype
The design and development of the proposed mobile robotic system is based on
total Mechatronic approach. This involves the integration of a number of classical
engineering disciplines namely, the mechanical, electrical/electronics and
computer-based control.
Mechanical: Critical design process of the mechanical aspect should be initiated
to come up with the best ever possible product design of the robot. The
mechanical system should comprise the base structure, wheel mechanisms,
transmission drive system, main body, chassis, mounting, work table and a
manipulator with special gripper attachment at the end of the arm. The design
process will include conceptual and final design of the robot involving the
development suitable mechanisms, static and dynamic analysis of the structure of
the system, selection of materials and others which are all referred to and should
comply with the pre-determined design criterion. The design of the wheel
mechanisms are of particular importance in view of the mobility and
maneuverability aspects. The design should also take into account the ease of the
fabrication of the parts to be processed.
Electrical/electronics: The selection of the drive and actuator system should be
based on the force analysis of the system to ensure proper actuation of the system
is achieved. DC servo motors with suitable transmission drives are expected to be
used in the system. The actuators should be driven by a set of suitable power
6
packed portable batteries. The essential electronics involve the incorporation of
the motor drivers, sensory and signal conditioning devices. A number of sensors
are used and placed strategically in the system. Inductive sensor is installed to
provide sensing signal related to the guidance system. Another additional feature
to be incorporated in the system is the vision system involving the use of CCD
camera and image processing software The AFC scheme specifically uses a
current sensor and accelerometer to obtain the measured values of the parameter
necessary for the control action. The signal conditioning aspect utilizes a number
of circuits such as those related to amplification/attenuation, buffer, active filters,
and analog-to-digital (A/D) and digital-to-analog (D/A) conversions.
Computer-based control: The microprocessor-based control will ultimately
implement the embedded system technology. Initial work will involve the use of
PC-based devices and software to control the system. At a later stage, this will be
transformed to wireless and fully autonomous system with suitable embedded
components.
iv. Experimentation
Upon complete integration of the system components and hence the working
prototype of the WMR, experimentation will be rigorously carried out to test the
effectiveness of the proposed system. The tests will take into account various
operating and loading conditions.
v. Performance evaluation and analysis
Finally the system’s performance will be critically evaluated and analysed. This
includes the results obtained from both the simulated and prototype developmental
activities. The research outcomes should provide insights and information which
would be useful for future development, improvement and expansion of the system.
In addition to that, suggestion for further research works will also be outlined.
7
1.6 Organization of Report
The report is organized into eight chapters. In Chapter 2, the fundamental
concepts, underlying theories and reviews of the main topics of research pertaining to
modelling of the kinematics and dynamics of the mobile manipulator and their
control, resolved-motion-rate-control (RMRC) and resolved acceleration control
(RAC), active force control (AFC), fuzzy logic (FL) and knowledge-based system
(KBS), motion planning and virtual reality (VR) are described. The modelling of the
mobile robot systems comprising the platform and arm is first described as this
provides the basis for the simulation of the control system. Next, the principles of the
well known RAC and the pure AFC method is discussed with special attention
focused on the method to enhance the strategy using intelligent means, namely FL
and KBS methods. The KBS inference mechanism, i.e. knowledge investigation and
validation, knowledge representation, knowledge acquisition and knowledge
processing are discussed as well as the KBS procedures. A preliminary discussion on
the use of knowledge-based method to a fuzzy system is also addressed. A VR
technique is highlighted and introduced in this section.
Chapter 3 is on ωv -AFC with FL method. In this chapter, an inertia matrix
estimation method using fuzzy logic for an AFC scheme is presented. The fuzzy
logic mechanism computes the estimated inertia matrix (IN) automatically and
continuously, while the mobile robot is tracking the reference trajectory. The
performance of the proposed ωv -AFC-fuzzy logic control method is compared to
the ωv -AFC control scheme which has adopted the crude approximation technique
in the estimation of IN.
Chapter 4 elaborates the application of a VR technique applied to an AFC
method for the motion planning and control of a WMR in computer integrated
manufacturing (CIM) setting. The first section of the chapter touches on a description
of the robot simulator and highlights the overall architecture of the proposed virtual
WMR simulator. This is followed by the construction of the scene graph for the
virtual environment (VE) of the mobile robot’s workspace (layout). In addition, the
elements within the scene graph will be also briefly discussed. The simulation study
8
based on some of the theoretical concepts and principles derived from previous
chapters are fully described in this chapter. On top of that, a collision avoidance
algorithm is included in the chapter for the intelligent motion path planning of the
system.
Chapter 5 describes a simulation study of the new proposed scheme known as
Resolved Acceleration Control and Active Force Control (RACAFC) which employs
a crude approximation on the inertia matrix estimation. This proposed scheme is
considered as the basic robust motion control using AFC applied to the mobile
manipulator that deals with the integration of the robot’s kinematics and dynamics.
The tuning procedure of the inertia matrix estimator for both the mobile platform as
well as for the manipulator is rigorously discussed in this chapter. Some disturbances
were introduced to test the robustness of the proposed scheme.
Chapter 6 presents a simulation study of the main proposed scheme, i.e.,
Resolved Acceleration Control and Knowledge-Based Fuzzy Active Force Control
(RAC-KBFAFC). The complete procedure to realize the knowledge-based fuzzy
including the procedures of knowledge investigation, validation, representation,
acquisition and processing is sufficiently discussed. The procedure to investigate the
knowledge through appropriate acquisition process is highlighted. The knowledge
shall be used as the reasoning to design the proper fuzzy output function in the
development of the fuzzy rules inference mechanism applied to estimate the IN of
the system. This chapter also presents the complete results of the simulation study of
RAC-KBFAFC scheme that is subjected to a number of conditions.
Chapter 7 describes the mechatronic design and development of the
experimental mobile manipulator in the form of a working prototype comprising a
differentially driven mobile robot/platform with a two-link planar robot arm mounted
on the top of the platform. The system is equipped with graphical and real-time
monitor (RTM) control programming feature. This chapter also elaborates the
programming and experimental procedure based on the RAC, RACAFC and
RACKBFAFC schemes. The experimentation shall provide a basis for validating the
theoretical (simulation) counterpart.
9
Finally, Chapter 8 concludes the research project. The directions and
recommendations for future research works are also outlined in this chapter. Some of
the additional materials pertaining to relevant algorithms, computer programs or
modules, publications and achievements related to the research are enclosed in the
appendices.
CHAPTER 2
THEORETICAL FRAMEWORKS AND REVIEW
2.1 Introduction
This chapter is concerned with the description of various theoretical concepts
and literature that are directly related to the undertaken research. These are
specifically stated as the kinematic and dynamic and modelling of the mobile
manipulator and their control, resolved-motion-rate control (RMRC), resolved
acceleration control (RAC), active force control (AFC), fuzzy logic (FL),
knowledge-based system (KBS), motion path planning and virtual reality (VR)
technique. The proposed AFC-based schemes that are described in succeeding
chapters both for the simulation and experimental works shall utilize in parts or full,
the various concepts outlined in this chapter through suitably designed procedure and
implementation.
2.2 Mathematical Modelling of Mobile Manipulator
The modelling of the mobile manipulator is important prior to any simulation
work that may include the control element. This shall be duly described in the
subsequent sections in terms of the dynamic and kinematic aspects.
11
2.2.1 Dynamics of Mobile Manipulator
Recall the dynamics of a mobile manipulator obtained using the Lagrangian
approach that is subjected to kinematic constraints in the form (Lin, 2001):
ττλ )()(),(),()( qBqAqqFqqqCqqM dT =++++ &&&&& (2.1)
where the kinematic constraints are subjected to:
0)( =qqA & (2.2)
pq ℜ∈ represents the p generalized coordinate, ppqM ×ℜ∈)( is a symmetric and
positive definite inertia matrix, ppqqC ×ℜ∈),( & denotes centripetal and Coriolis
matrix, pqqF ℜ∈),( & is friction and gravitational vector, prqA ×ℜ∈)( is a
constraint matrix, rℜ∈λ is the Lagrange multiplier which represents the vector of
constraint forces, pd ℜ∈τ is a bounded unknown disturbances including
unstructured dynamics, )()( rppqB −×ℜ∈ is the input transformation matrix, and rp −ℜ∈τ represents torques input vector. If generalized coordinates q are described
into two sets, i.e. qv of the mobile platform and qr of the manipulator, ( )TTr
Tv qqq ,=
where mvq ℜ∈ are the generalized coordinates in the kinematic constraints of
Equation (2.2), and nrq ℜ∈ are the generalized coordinates of the local manipulator
system without kinematic constraints, then Equation (2.2) can be simplified into:
0)( =vvv qqA & with mrvv qA ×ℜ∈)( , (2.3)
with r is the kinematic constraints.
The following properties hold in Equation (2.1) (Lewis et al., 1999):
Property 2.1 (Parameter Boundedness):
12
qqCqqC
IMqMIM
b
pp
&& )(),(
)( maxmin
≤
≤≤
(2.4)
where Mmin and Mmax are the positive scalar constants that are dependent to the
robot’s mass properties and constraint matrix, Ip is a p×p identity matrix, and )(qCb
is a positive function of q. In this thesis all of the joints are assumed to be revolute so
that )(qCb is a finite positive constant (Lewis et al., 1993).
Property 2.2 (Skew Symmetric):
T
T
CCM
CMCM
+=
−−=−
&
&& )2(2 (2.5)
By implementing Equation (2.3) and separating the generalized coordinates
into two sets, ( )TTr
Tv qqq ,= Equation (2.1) can be rewritten as
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
r
vv
dr
dvvTv
r
v
r
v
r
v
BqA
FF
CCCC
MMMM
ττ
ττλ
0)(
2221
1211
2221
1211
&
&
&&
&&
(2.6)
where rmv
−ℜ∈τ is the actuated torque vector of the constrained coordinates that
subject to nonholonomic constraints, )( rmmvB −×ℜ∈ is input transformation matrix of
the mobile platform, dvτ , drτ , Fv, and Fr are torque disturbances and frictions and
gravity vector for mobile platform and manipulator respectively. The properties
related to Equation (2.6) can then be expressed as:
Property 2.3 (Skew Symmetric):
13
T
T
CMCM
CMCM
)2(2
)2(2
22222222
11111111
−−=−
−−=−
&&
&&
(2.7)
Property 2.4:
T
T
MM
CCM
2112
122121
=
+=&
(2.8)
By considering Equation (2.3) as the equation subject to the standard matrix
theory a full rank transformation matrix )()( rmmvv qS −×ℜ∈ which spans the null space
of )( vv qA can be defined as
0)()( =vTvv
T qAqS (2.9)
where )( vqS is bounded at ς≤)( vqS with ς is positive number. Note that )( vv qA is
bounded. From Equation (2.9), an auxiliary vector of the platform velocity rmtv −ℜ∈)( can be obtained in the form
)()( tvqSq vv =& (2.10)
then, in the form of acceleration mode or its derivative is given by:
vqSvqSq vvv )()( &&&& += (2.11)
From Properties 2.1 and 2.2 and by considering Equations (2.1) and (2.11),
additional properties can be defined (Lin and Goldenberg, 2002) as follows:
14
Property 2.5:
bb
bbT
MMMM
MMMSMS
22222121
12121111
≤≤
≤≤
(2.12)
where bM11 , bM12 , bM 21 , bM 21 are positive constants that are assumed to be
unknown.
Property 2.6:
qCCqCC
qCCqCSCS
bb
bbT
&&
&&
21212222
12121111
≤≤
≤≤
(2.13)
where bC11 , bC12 , bC21 , bC21 are positive constants.
Generally, Equations (2.6) and Equation (2.10) describe the dynamic
equations of the mobile manipulator that subject to kinematic constraints. These are
used to design the proposed motion control of the robot system that deals with the
kinematics and dynamics.
2.2.2 Kinematics of Mobile Manipulator
Figure 2.1 (a) shows the mobile platform moves by driving the two
independent wheels (left and right). In the figure, XY is the world coordinate system,
xy is the robot coordinate system, φ is the robot’s heading angle, 2b is the width of
the robot, r is the radius of the wheels, and d is the distance of point G to F. It is
assumed that the velocity at which this system moves is relatively slow and therefore
the two driven wheels do not slip sideways. The velocity of the platform center of
15
mass, vG, is then perpendicular to the wheel axis. This expresses x and y components
in a nonholonomic equation as follows:
0cossin =− ϕϕ GG yx && (2.14)
For point F, the constraint can be written as:
0cossin =+− dyx FF ϕϕϕ &&& (2.15)
where d is the distance between G and F.
X
Y
F
2b
r
φ
y x d
(xF, yF) ? G
X
Y
F
2b
r m1, I1 θ1
θ 2
φ
(xE, yE)
y x d
E
(xF, yF)
m2, I2
m0, I0 ? G
?
?
l2
l1 l11
l22
(a) (b)
Figure 2.1: (a) A mobile platform and (b) A mobile manipulator
Following Papadopoulos and Poulokakis (2000) and considering Equation
(2.15), the general coordinate system, TFF yxq ],,[ ϕ= of the robot assuming that its
wheels roll and do not slip, the direct kinematic can be expressed as:
⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
R
Lvv
F
F
F
qSyx
θθ
ϕ&
&
&
&
&
)( or )()()( tqStq vv θ&& = (2.16)
and its inverse kinematic is:
16
)()()( 1 tqqSt v && −=θ (2.17)
where Sv(qv) is derived from Figure 2.1 (a) as:
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
−
⋅+
⋅−
⋅−
⋅+
=
br
br
brdr
brdr
brdr
brdr
qS vv
22
cos2
sin2
cos2
sin2
sin2
cos2
sin2
cos2
)( ϕϕϕϕ
ϕϕϕϕ
(2.17)
and Lθ& , Rθ& are the angular velocities of the left and right wheel respectively.
Equation (2.16) can be rewritten as:
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
−
⋅+
⋅−
⋅−
⋅+
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
R
L
F
F
F
br
br
brdr
brdr
brdr
brdr
yx
θθ
ϕϕϕϕ
ϕϕϕϕ
ϕ&
&
&
&
&
22
cos2
sin2
cos2
sin2
sin2
cos2
sin2
cos2
(2.18)
Equation (2.18) can be expressed in the form of rotation matrix as follows:
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⋅⋅−
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=⎟⎟
⎠
⎞⎜⎜⎝
⎛
R
L
F
F
brd
brd
rr
yx
θθ
ϕϕϕϕ
&
&
&
&
22
22cossinsincos
(2.19)
For the manipulator serially mounted on board the platform at point F as in
Figure 2.1 (b), its forward kinematic can be described as:
⎟⎟⎠
⎞⎜⎜⎝
⎛ +⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛ −+⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
2
1
2221
1211
cossinsincos
θϕθ
ϕϕϕϕ
&&&
&
&
&
&
JJJJ
yx
yx
F
F
E
E (2.20)
17
where
)sin(sin 2121111 θθθ +−−= llJ (2.21)
)sin( 21212 θθ +−= lJ (2.22)
)cos(cos 2121121 θθθ ++= llJ (2.23)
)cos( 21222 θθ += lJ (2.24)
Equation (2.20) indicates that the kinematic control of the two sub-systems
(platform and manipulator) can be partially solved. It is sometimes very useful to
analyze the singularity of the system when the robot arm is out of reach beyond its
workspace. If (xF, yF) is assumed to be in fixed position (platform is not moving and
hence ϕ& = 0), Equation (2.20) can be expressed as:
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
2
1
2221
1211
θθ&
&
&
&
JJJJ
yx
T
T (2.25)
where (xT, yT) is the tip position coordinate relative to the workspace of the
manipulator. Then its inverse kinematic is:
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛ −
T
T
yx
JJJJ
&
&
&
& 1
2221
1211
2
1
θθ
(2.26)
Substituting Equations (2.19), (2.21), (2.22), (2.23) and (2.24) into Equation
(2.20) and letting TEEFF yxyxq ],,,[= as the input reference coordinate, the complete
direct kinematic equation of the mobile manipulator is given by:
18
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−
++−
+−
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
2
1
22212121
12111111
00
0022
)()(22
cossin00sincos0000cossin00sincos
θθθθ
ϕϕϕϕ
ϕϕϕϕ
&
&
&
&
&
&
&
&
R
L
F
F
E
E
brd
brd
rr
JJbrJd
brJd
JJbrJr
brJr
yxyx
(2.27)
where Lθ& and Rθ& are the angular velocities of the left and right wheels respectively,
1θ& and 2θ& are the angular velocities of the joint angle of link-1 and link-2
respectively.
Letting a full rank transformation matrix S(q) in Equation (2.27) as:
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−
++−
+−
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−
=
00
0022
)()(22
cossin00sincos0000cossin00sincos
)(
22212121
12111111
brd
brd
rr
JJbrJd
brJd
JJbrJr
brJr
qS
ϕϕϕϕ
ϕϕϕϕ
(2.28)
the direct kinematic equation can be expressed as:
19
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
2
1
)(
θθθθ
&
&
&
&
&
&
&
&
R
L
F
F
E
E
qS
yxyx
(2.29)
and its inverse kinematic is:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−
F
F
E
E
R
L
yxyx
qS
&
&
&
&
&
&
&
&
)(1
2
1
θθθθ
(2.30)
2.2.3 Dynamics of Mobile Platform
Assume that Equation (2.6) represents the dynamic model of the mobile
manipulator in Figure 2.1. Expressing the first m-equations in Equation (2.6) yields:
vvdvTvvrvrv BAFqCqCqMqM ττλ =++++++ &&&&&& 12111211 (2.31)
Multiplying both sides of Equation (2.31) by ST and using Equation (2.9) to eliminate
the constraint force we obtain:
vvT
dvTT
vT
vT
rT
vT
rT
vT
BSSAS
FSqCSqCSqMSqMS
ττλ =++
++++
12111211 &&&&&&
or
vvT
dvT
vT
rT
vT
rT
vT
BSS
FSqCSqCSqMSqMS
ττ =+
++++
12111211 &&&&&&
(2.32)
Substituting both Equations (2.10) and (2.11) into Equation (2.32) yields
20
vvT
dvT
vT
rTT
rTTT
BSSFS
qCSSvCSqMSvSMSvSMS
ττ =++
++++
1211121111 &&&&&
(2.33)
To simplify the expression, Equation (2.33) can be rewritten as:
dvvv fvCvM ττ +++= 1111 & (2.34)
where SMSM T1111 = (2.35)
SMSSCSC TT &111111 += (2.36)
dvT
dv S ττ = (2.37)
vvT
v BS ττ = (2.38)
)( 1212 vrrT
v FqCqMSf ++= &&& (2.39)
Component fv consists of gravitational and friction force vector Fv, and the dynamics
interaction with the mounted manipulator (i.e., rr qCqM &&& 1212 + ). Let us consider the
mobile platform as in Figure 2.1 (b). Assuming the dynamics interaction with the
mounted manipulator is very small (the arm moves at low speed) and the platform
moves in a horizontal XY Cartesian coordinate, the component fv can be neglected.
Therefore, Equation (2.34) can be rewritten as:
dvv vCvM ττ ++= 1111 & (2.40)
or in the form of q generalized coordinates (Fukao et al., 2000):
QqqqVqqMqB ++= &&&& ),()()( τ (2.41)
where Q are the bounded unknown disturbance torques that could include the
unstructured mobile platform dynamics. The matrices, )(qM , )(qV and )(qB can
be described respectively as:
21
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
++−
−++=
w
w
IImbbrImb
br
ImbbrIImb
br
qM)(
4)(
4
)(4
)(4)(
22
22
2
2
22
22
2
2
(2.42)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−=
02
20
),( 2
2
ϕ
ϕ
&
&&
dmb
r
dmb
r
qqVc
c (2.43)
⎥⎦
⎤⎢⎣
⎡=
1001
)(qB (2.44)
where the mass of the total system, wc mmm 2+= with mc is the mass of the body,
mw is the mass of the wheel, mcwc IIbmdmI 22 22 +++= , and Ic is the moment
inertia of body about the vertical axis thru G, Iw is the moment inertia of the wheel
and motor about the wheel axis, and Im is the moment inertia of the wheel and motor
about the wheel diameter.
2.2.4 Dynamics of Manipulator Arm
Expressing the first n-equations in Equation (2.6), i.e. the equations related to
the manipulator, yields:
rdrrrvrv FqCqCqMqM ττ =++++++ 022212221 &&&&&& (2.45)
To clarify the dynamic interaction term, Equation (2.39) can be rearranged as:
rdrrvvrr FqCqMqCqM ττ =+++++ )( 21212222 &&&&&& (2.46)
where the terms in the brackets, i.e. )( 2121 rvv FqCqM ++ &&& , are the dynamic
interaction with the mobile platform and the gravitational and friction force vector.
22
For the manipulator with a planar configuration and moves in a horizontal XY
Cartesian coordinate and the dynamic interaction is very small (the platform moves
slowly), the component within the brackets in Equation (2.46) can be neglected so
that it can be expressed as:
rdrrr qCqM ττ =++ &&& 2222 (2.47)
Equation (2.47) can be rewritten as:
rdrrr qqqhqqH ττ =++ &&&& ),()( (2.48)
where
⎥⎦
⎤⎢⎣
⎡=
2221
1211)(HHHH
qH (2.49)
and ⎥⎦
⎤⎢⎣
⎡=
2212 sin0
),(θcllm
qqh & (2.50)
with ( ) 222122
2121
21211 cos2 mcccmc IllllmIlmH +++++= θ (2.51)
222222122112 cos mcc IlmllmHH ++== θ (2.52)
222222 mc IlmH += (2.53)
2.2.5 Kinematic Control of Mobile Manipulator
There are a number of extensive works that can be found in literature related
to the kinematic of the mobile manipulator (Wang and Kumar, 1993, Perrier et al.,
1998, Bayle et al., 2001, Papadopoulos and Poulakakis, 2001, Sugar and Kumar,
2002, and Tanner et al., 2003). The works mostly focus on the methods to solve the
redundancy problems with the dynamic not specifically addressed. The kinematic
analysis is particularly useful to describe the robot’s workspace and motion path
23
planning tasks including obstacles avoidance, collision free moving capability and
manoeuvrability. Wang and Kumar (1993) used instantaneous (local) and global
approaches of a screw-theoretic formulation to solve the redundancy of the robot
motion. The basic of their works is the use of joints compliances analysis to resolve
the redundancy. However the joint compliances model output equations resulted
were not the Jacobian matrix of a kinematics function therefore it could not be
directly applied to the nonholonomic system. The way they reformulated was by
imposing additional constraints of the holonomic system so that the resulting system
was holonomic. The screw-theoretical formulation approaches used in their works
was found to be a theoretical significance although the approaches are relatively not
the simple way to be chosen.
Kanayama, et al. (1990) proposed a stable tracking control method for an
autonomous mobile robot. The major objective of the control rule is a method to
find a reasonable target, linear and rotational velocities Tv ),( ω . The stability of the
control rule is proven using a Lyapunov function. According to Kanayama, one of
the difficulties of the mobile robot problem lies in the fact that ordinary vehicles
groups only two degrees of freedom (linear velocity and angular velocity) for
locomotion control, although vehicles have three degrees of freedom, x , y and θ in
its positioning. Another difficulty is in the non-linearity of the kinematic relation
between Tv ),( ω and Tyx ),,( θ&&& . The use of a Lyapunov function also resolves these
difficulties. Linearizing the system’s differential equation is useful to decide
parameters for critical dumping for a small disturbance. This equation is very
popular in mobile robot literatures and has become a ‘standard reference’ by many
researchers.
Perrier et al. (1998) implemented homogenous matrices and dual quaternion
to represent the redundancies in the kinematics problems. They considered the global
motion of mobile manipulator from point to point and computed a path that takes
into account different constraints; the nonholonomic and holonomic. Their works
were successfully resolved the redundancy of the kinematics problem in joints
limitation, velocity and radius steering limitations although they didn’t explain the
24
experimental results in their paper. Bayle et al. (2001) focused the investigation on
the manipulability of a particular class of mobile manipulator in local kinematics
analysis. They showed how the notion of manipulability could be extended to
represent the operational methods in a configuration of the system. One of the
advantages of their works is that it can be used to reconfigure the installed robot arms
position on the top of the platform in order to maximize the workspace operations.
Papadopoulos and Poulakakis (2001) presented a robot trajectory tracking
method with obstacle avoidance capability using conventional inverse kinematics
control based on velocity control added by obstacle mapping formulation. In the
paper they successfully showed the smooth effect and continuous function of
trajectory tracking as well as polynomials characteristic and the simplicity in
implementation of their scheme thru simulation. However, only the known obstacle
location and fixed position can be considered because of the robot was not described
to have self obstacle mapping algorithm. Sugar and Kumar (2002) developed a
kinematics-based control of multiple mobile manipulators. Their analysis was based
on tasks that require grasping, manipulation and transporting large and possibly
flexible objects without special purpose fixtures. The kinematics problems were
solved using the compliant arms analysis and it was successfully demonstrated in the
paper for cooperation of two and three mobile manipulators. They also addressed an
integrated force controller in their proposed scheme for each robot using force or
stiffness control for the actively arms. They reported that the use of the force
controller that affects the internal forces and moment on the box (the object handled)
was successfully controlled, but the accuracy of the system was poor due to large
orientation errors of the object.
Tanner et al. (2003) proposed a new methodology to motion planning for
multiple mobile manipulators cooperation that applicable for articulated, non point
nonholonomic robots with guaranteed collision avoidance and convergence
properties. They implemented a potential field technique using diffeomorphic
transformations and the resulting point-world topology. Their approach was applied
on multiple mobile manipulators to handle deformable material in an obstacle
environment and it showed the success thru simulation. The main feature of their
25
method is application of dipolar potential field technique to guarantee the robot will
approach the destination asymptotically and it will follow the path that automatically
stabilizes its orientation. This method incorporated an inverse Lyapunov function to
stabilize (and converge) the robots navigation. Their works are found very useful for
future developments in coordinated kinematics controls, but unfortunately they did
not address the robustness of each robot specifically.
2.2.6 Dynamic Control of Mobile Manipulator
In actual implementation pertaining to robot’s motion, it is also typical to
address the control problem involving the robot’s dynamic. At this juncture,
designing appropriate controller can lead to significant improvement in performances
(Yamamoto and Yun, 1996). Combining both the extensive kinematic and dynamic
aspects for a perfectly motion control of any dynamical system still remains a
complex and challenging problem. In recent years, several researchers have
contributed to solving this problem using a number of methods such as those related
to adaptive (Colbaugh, 1998), optimal (Mohri et al., 2001), neural network (Lin and
Goldenberg, 2001), and model-based (Papadopoulos and Poulokakis, 2000) control
schemes. Yamamoto and Yun (1996) rigorously modeled the dynamics coupled and
interaction between mobile platform and manipulator. They have investigated the
dynamics interactions when the manipulator executing the task and the platform has
followed a specified trajectory. The aim of their work was how to actively
compensate the dynamic interaction that influences to the robot performance using a
class of non-linear feedback control. The feedback control was based on state space
model. In the paper, they showed the successful implementation of the technique to
mobile manipulator by way of simulation.
Colbaugh (1998) addressed the problem of stabilizing mobile manipulators in
the presence of uncertainties regarding the system dynamic model. He proposed an
effective solution by combining homogenous system theory and adaptive control
theory. His proposed scheme contains of two subsystems, i.e. a homogenous
kinematic stabilization strategy which derived a desired velocity based trajectory,
26
and an adaptive control scheme which ensures that the velocity based trajectory is
accurately tracked. Mohri et al. (2001) presented a trajectory planning method using
an optimal control theory. They derived the robot’s dynamics by considering it as a
combined system of mobile platform and manipulator. Then they applied a sub-
optimal trajectory planning using an iterative algorithm based on gradient functions
synthesized in the hierarchical manner to formulate the trajectory-planning problem.
They reported the effectiveness of the scheme by simulation. One of the advantages
is the simple trajectory planning modification needed when an obstacle is considered
in the workspace. Nevertheless they did not state the overall system robustness
specifically in the paper.
Lin and Goldenberg (2001) proposed a class of neural network (NN) control
of mobile manipulator that is subjected to kinematics constraint. They assumed that
the robot’s dynamic is completely unknown and it would be identified using a neural
network estimator. For the trajectory tracking control they used a class of feedback
control that its stability was tested using a Lyapunov function theory. They have used
a procedure to estimate the dynamics as follows: First, the robots dynamics were
redefined as an error dynamics based on a set of carefully chosen Lyapunov sub-
functions through a joint-space tracking. Next, a NN on-line estimator was
constructed and a new-NN learning law was obtained after which a new NN control
could be derived. From the simulation, they were able to demonstrate the
effectiveness of their proposed scheme.
Papadopoulos and Poulokakis (2000) used a model-based approach to derive
the control of mobile manipulator. The robot dynamics was assumed to be
completely known. They did not use any specific robust control scheme incorporated
into the motion control except the error-based feedback control that consider the
dynamics coupling of the mobile platform and the manipulator. The robustness of the
system was not specifically guaranteed because they only applied the position and
velocity orientation.
27
2.3 Resolved Motion Rate Control and Resolved Acceleration Control
Resolved Motion Rate Control (RMRC) in robotic means that the motions of
the various joint or degrees of motors are combined and resolved into separately
controllable motions along the world coordinate axes (Fu et al., 1987). This implies
that the motors must run simultaneously at different time-varying rates in order to
achieve the coordinated motion in the workspace. The parameters controlled could
be parts of the order of the control system, i.e. position, velocity and or acceleration.
In feedback control system, the resolved motion control can be grouped in two types,
i.e. resolved motion rate control (RMRC) and resolved motion acceleration control
(RMAC). The second is often simply described as resolved acceleration control
(RAC). The main difference of the methods is that the RMRC employs position and
velocity orientation as the controlled parameters only while the RAC also
incorporates acceleration signals in order to achieve a more stable control.
RobotSystem
External Forces
(Disturbances)
RMRC
PositionSensor
Position Ref
+ - Velocity/Rate
Sensor
Velocity/Rate Ref
+ -
y
s1
Figure 2.2: A schematic diagram of RMRC
A schematic diagram of RMRC is illustrated in Figure 2.2. The figure depicts
the input functions consisting of velocity/rate and position. This implies the users can
specify any position and rate of each motor/actuator independently. In contrast, a
simultaneous velocity and position calculation should be done carefully.
Nevertheless, the RMRC is still one of the simplest motion controls that is selected
by a number of researchers in the last decade including RMRC using fuzzy logic
(Kim and Lee, 1993), singularity free RMRC (O’neil et al., 1997) and inverse
28
kinematic learning for RMRC applied to a humanoid robot (D’souza et al., 2001).
Luh et al. (1980) introduced an extension to the RMRC by incorporating acceleration
command vectors in the schematics. The scheme was popularly known as resolved
motion acceleration (RMAC) or simply resolved acceleration control (RAC). The
general form of the RAC in robotics can be illustrated as shown in Figure 2.3.
External
Forces (Disturbances )
RMAC/RAC
Position Ref
+ -
Vel/Rate Ref
Acceleration Sensor
- +
- +
Acceleration Ref
y
s1
s1
PositionSensor
Velocity/RateSensor
RobotSystem
Figure 2.3: An illustration of the RMAC/RAC schematic diagram
Muir and Neumann (1990) investigated the use of RMRC and RAC in a
mobile robot control. They were able to apply the RAC scheme in a mobile robot
system and it was demonstrated that RAC was superior compared to RMRC.
Kircanski and Kircanski (1998) reported a rigorous investigation of RMRC and RAC
applied to a damping-based braking system with actuators constraints. They have
showed that the addition of braking system to the RAC was found to be more
effective than before. Campa et al. (2001) proposed a method to prove the local
asymptotic stability of RAC applied to robot manipulator control by invoking a strict
Lyapunov function. They concluded that the motion control of the manipulator in
task space and whose pose of the end-effector is of some concern, could be solved by
the RAC technique.
From the above reports, it is obvious that the RAC is still one of the best
control options due to its simplicity in real-time implementation. In the study, the
RAC is developed as the integrated simplified mobile platform coordinate and
29
heading angle, (xv, yv, φ) control and the XY Cartesian planar manipulator’s tip
position coordinate, (xm, ym) control. By using this technique, the proposed control
scheme would have a more flexible position, speed and acceleration control. This
flexibility is gained by the use of simultaneous input reference position, velocity and
acceleration parameters.
2.4 Active Force Control (AFC)
Hewit and Burdess (1981) first applied the technique known as active force
control (AFC) successfully to a robotic arm. They proposed a practical and robust
technique to compensate for the internal and external disturbances of a
mechatronics/machinery system by employing an internal force error feedback
control based on real-time acceleration and force measurements. The general form of
the AFC scheme is depicted in Figure 2.4.
IN/Ktn Ktn
1/Ktn
MobileManipulator +
+
TqQ
Q*
-+
++θref
IN
θact.. ..
Figure 2.4: Typical AFC loop
The important AFC algorithm is defined as follows:
Q* = Tq - IN actθ&& (2.56)
where actθ&& is the actual acceleration signal, Tq is the torque applied, Q is known and
unknown (bounded) internal and external disturbances including payloads, Q* is the
30
estimated disturbances observed and IN is the estimated inertia matrix, approximated
by suitable means. In the figure, refθ&& is the reference acceleration signal and Ktn is the
motor torque constant. The aim of the AFC method is to ensure that the system is
stable and robust even in the presence of known or unknown disturbances. The main
advantage of the method is that it can give a compensating action using mainly the
estimated or measured values of certain parameters. This method has the benefits of
reducing the mathematical complexity of the robot system that is known to be highly
coupled and non-linear. However, AFC could not solve the motion control of robotic
system by itself without incorporating a lower order of control, i.e., position and or
velocity control, typically located in the outermost loop. The scheme depicted in
Figure 2.4 is an open loop mode of control so that it should be combined with a
proper feedback (tracking) control in order to achieve a complete motion control.
One of the alternatives is by implementing the RAC scheme to the AFC which is one
of the proposed schemes implemented in the research. Figure 2.5 shows the concept
of a RAC combined with AFC that is applied to a robot system. In the figure, the
RAC is depicted to contain in the left dashed box. Input references in the RAC
consist of position (xbar), velocity (xdbar) and acceleration (xddbar) that are all subjected
to the workspace of the coordinate system. The right dashed box contained in the
figure indicates the AFC part. H denotes the dynamic constraint of the robot system.
The main computational burden in AFC is the multiplication of the estimated inertia
matrix with the respective acceleration of the robot dynamic component before being
fed into the AFC feed forward loop.
IN/Ktn Ktn
1/Ktn
H-1 1/s 1/s
IN
θ ddref
++
Ic Tq
Q
Q*
-+
++coordinate
transformation
K d K p
coordinate transformation
coordinate transformation
θ θ d θ ddIt
Ia
x ddref x ddbar
x dbar
x bar
+
+
-
-
+ +
+ +
x d
x
AFCRAC
Figure 2.5: RAC combined with AFC
31
A number of implementations of the AFC schemes applied to robotic
manipulator can be found in Hewit and Marouf (1996), Musa (1998), Hewit and
Morris (1999) and Pitowarno et al. (2001). In other forms, the basic AFC scheme
was further studied and modified by a number of researchers and can be found in
works by Uchiyama (1989), Ohnishi (1995), Komada et al. (1996), and Godler et al.
(2002). The term ‘disturbance observer control’ as a class of the modified AFC was
typically used in literature. Some of their proposed modified AFC schemes were
successfully implemented in real world applications.
2.4.1 Estimated Inertia Matrix
As mentioned earlier, one of the main problems in AFC scheme is how to
acquire the appropriate estimated inertia matrix so that the compensation of the
disturbances can be effectively carried out. Actually, the inertia matrix of the robotic
system when operated is highly non-linear that can be caused by payloads, noise,
frictions such as static, coulomb, and viscous friction, vibrations and other unknown
disturbances. Supposed that the system has relative small disturbances (inherent
noise at sensors and or actuators, low friction at joint and no/small vibration), so the
appropriate inertia matrix can be sought using basic approximation techniques.
Basically, the inertia matrix of a specific robotic system - for example two-link
planar robotic arm – can be heuristically introduced first with a certain value by
considering the system and mass properties.
The application of AFC to a planar two-link robotic arm using the basic
(crude) approximation technique was successfully presented (Musa, 1998). The
tested robot system has the estimated inertia matrix expressed in the following form:
⎥⎦
⎤⎢⎣
⎡=
2221
1211
ININININ
IN (2.55)
and IN = Ki H (2.56)
32
where the off-diagonal elements IN12 = IN21 = 0.
Although the most appropriate inertia matrix estimator should indicate
properties of “non-linearity” of the value following the high non-linearity of the
system operation – not a fixed value, Ki, as in Equation (2.56) – however this basic
multiplier constant as an estimator was sufficiently exposed the powerful of the AFC
in the application (Musa, 1998).
2.4.2 Estimation of Inertia Matrix using Intelligent Schemes
Some estimation of the inertia matrix techniques applied to robotic systems,
mostly to robotic arm systems, were successfully implemented, such as using
Acceleration Tracing Orientation Method (ATOM) (Komada and Ohnishi, 1990),
disturbance observer and inertia identifier in task space (Komada, et al., 1996). In
particular, also in a robotic arm system, the robustness of control schemes with
disturbance observer and with acceleration control loop was compared and reported
(Godler et al., 1999). So far there is no report related to applications of the inertia
matrix estimation technique of the AFC that is implemented to a mobile manipulator
system. In the case of planar two-link robotic arm, some implementations of
intelligent techniques for estimating the inertia matrix were presented, such as using
neural network (Musa, 1998), fuzzy logics (Musa and Nurul, 2000), iterative learning
(Musa and Hooi, 2000), and knowledge-based method (Pitowarno, 2002). The
rationale of using the intelligent mechanism is to compute the required inertia matrix
automatically, continuously and on-line. However, the using of these intelligent
techniques in the AFC was merely dealt with the robotic arm only. In the research
work the estimation of the inertia matrix on a more complicated robotic structure, i.e.
the mobile manipulator system would be intensively investigated. In the subsequent
chapters a class of iterative learning and knowledge-based fuzzy algorithms as the
inertia matrix estimator of the robot which is proposed in this study would be
relevantly described in the ensuing sections related.
33
2.5 Knowledge Based System
The term of knowledge-based system (KBS) is commonly used to represent a
system that work in case of handling all of the system aspect or operation that based
on a group of prior knowledge of the system’s characteristics, behavior,
environments and or all others information – or in the close term: knowledge - that
can be correlated to the system. In other point of view the KBS is a system with
mostly human-centered. If the human have expertise to interpret the knowledge to a
smart knowledge-based decision rules and this expertise to be represented to a
computer then the overall system may be described as an expert system.
Generally, the major component of a knowledge-based system is well known
as expert system. As mentioned previously, expert system is a term used to represent
an intelligent technique that is mainly based on the human expertise (the knowledge
of the expert) whether directly or indirectly. Soucek (1989) described some typical
engineering applications of expert systems in fault diagnosis, factory cell simulation,
knowledge-base robot and process control. These expert systems follow the concept
of Model-Based Reasoning that the model contains an explicit description of a
domain, objects, relationship between objects, and taxonomy of the object classes.
By the approaches, the expertise could be interpreted as rules expression that will be
used in the computer or controller programming.
Figure 2.6 shows an illustration of a generic expert system as mentioned by
Ignizio (1991). The components within the dashed box are those linked with the use
of computer or microprocessor. Outside this dashed box, access capabilities for two
types of human users are noted. The first one is the individual designated as the
knowledge engineer that is the person responsible for placing the knowledge into the
expert system’s knowledge base. He or she accomplishes this job through the
interface - as shown as directly interconnected, and the rule adjuster. The knowledge
engineer can also be the interface between the human expert and the expert system.
This means, the knowledge engineer somehow must capture the expertise of the
human expert and express it in a format or structure that may be stored in the
knowledge base memory that will be used by the expert system.
34
Knowledge Base
Rule adjuster
Inference Engine
Working Memory
I n t e r f a c e
UserKnowledge
Engineer
within the computer
Figure 2.6: An illustration of a generic expert system
Ideally, there would be no need for a knowledge engineer by assumption that
the domain expert would directly interact with the expert system. So the domain
expert would replace the knowledge engineer in the figure. The second type of
individual with access to the expert system is the user. This designation refers to
anyone who will use the expert system as a decision-making aid.
The interface handles all input to or output from the computer. Currently, the
interface becomes more sophisticated in line with advancement of computers’
technology. The input and output devices are already improved to meet the demands
of the multimedia and global networking era. The inference engine performs two
primary tasks. Firstly, it examines the status of the knowledge base and working
memory so as to determine what facts are known at any given time, and to add any
new facts that become available. Secondly, it controls the session by determining the
order which inferences are made. The knowledge base, as the heart of the expert
system, contains two types of knowledge, i.e., facts and rules. The working memory
is a memory device that the contents change according to the specific problem at
hand. Finally, the rule adjuster serves merely as a rule editor that enters the rules
specified by the knowledge engineer into the knowledge base during the
35
development phase of the expert system. In more sophisticated expert systems, the
rule adjuster may be improved by incorporating a learning algorithm in the process.
In particular, Young-Tack and Wilkins (1992) depicted that the KBS inference
mechanism could be an intersection of expert system (based on AI or Intelligent
Control methods), machine learning and probabilistic reasoning. Figure 2.7
illustrates this concept.
Figure 2.7: An illustration of KBS
The explanation using Figure 2.7 gives more precise meaning of KBS
inference mechanism. Each of the three parts of KBS could have particular domain
in research. Currently, designing an appropriate knowledge-based method to a
system not only needs expert system methodologies to realize, but however machine
learning algorithms are also needed to create knowledge includes rule adjuster
automatically. On the other hand, to ensure the validity of knowledge being collected
statistical based algorithms are also important to be influenced. Machine learning is
the study of computer algorithms that improve automatically through experience
(Mitchell, 1997). Applications range from data mining programs that discover
general rules in large data sets, to information filtering systems that automatically
learn user’s interests. Machine learning methods have been applied to problems such
as learning to drive an autonomous vehicle, learning to detect credit card fraud,
learning to recognize human speech, etc. The probabilistic reasoning as the third
group of the intersection, also gains through the exploration of the goal of KBS.
Probabilistic Reasoning
Machine Learning
KBS
Examples: Iterative Learning, Learning on Fuzzy/Neural Net Online-systems, adaptive control, etc.
Expert System Tools: Neural Network, Fuzzy Logics, Genetic Algorithm, Evolutionary Computation, and other AI methods.
36
Recently, in common application the KBS are designated to handle a large
amount of knowledge with complex interconnections that need a probabilistic
analysis to manage it. Thus, the KBS environment also needs the statistical
approaches to solve this problem. Some researchers focused the research on the
probabilistic analysis of KBS. Growe et al. (2000) described in detail how the
Bayesian Network could be implemented as a powerful tool to judge validity of the
knowledge base. In particular, the human expert supplies the observations of the
probabilities in any possible way. So, the accuracy of probabilities value (0 to 1) is
fully dependent on the statistical based observation of the data or knowledge being
collected. The human expert can use the analytical based and or survey based to set
this value. Hence, the accuracy of the analysis also depends on how valid the
probabilities being set.
Generally, the KBS procedures or mechanism consisted of knowledge
investigation and validation, knowledge representation, knowledge acquisition and
knowledge processing. From these procedures, the inference mechanism can be
developed and implemented by way of a computer program. In the last decade (1995
to 2004) expert system methodologies were rigorously investigated by researchers.
This implies the use of some terms in expert system domain, KBS and other human-
centered artificial intelligence (AI) method could be interchangeable. A survey that
indicated this development in expert system methodologies was reported by Liao
(2005). He has found that some existing terms often used by researchers to describe
the specific meaning in their expert system applications, such as rule-based system,
knowledge-based system, neural networks, fuzzy expert system, object-oriented
methodology, case-based reasoning, modeling and system architecture, intelligent
agents, ontology, and database methodology. It is usual that some of the terms like
‘rule-based’ and ‘knowledge-based’, ‘rule-based and fuzzy logic’ are interchangeable
and could be overlapping.
2.6 Fuzzy Logic
37
In general, a fuzzy logic (FL) concept as initiated by Zadeh (1988) attempts
to mimic human experts’ knowledge. It tries to imitate the human expert’s behavior
by computing with words. First, human words are depicted by membership of
functions (MFs). Secondly, qualitative human knowledge is contained in the rule
base. Then, experienced human reasoning is imitated by implication methods and the
inference engine. For the purpose of reviewing some principles of the equations used
in designing a fuzzy logic system, they will be explained briefly in the following
paragraphs.
Figure 2.8 shows a block diagram of a typical fuzzy logic system.
Figure 2.8: An illustration of a fuzzy logic system
The input space fuzzifier or MF has shape and parameters to design. The
shape at least consist of singleton, trapezoidal, Gaussian MF, while the parameters
provide support, crossover, and bandwidth. The input space partition at least has
options of uniformity and completeness. Users can choose these options of MF
depending on their needs and requirements. The rule base has typically two options,
i.e. fuzzy antecedent – fuzzy consequence and fuzzy antecedent – crisp consequence
(singleton or linear function). The equations of singleton, trapezoidal and Gaussian
MFs are given in Equations (2.57), (2.58) and (2.59) respectively.
Pre processing
fuzzy-fication
rule base(r rules)
inference engine
defuzzy-fication
Post processing
ki partitionsper input
system inputs
system outputs x i n U y in V
k outputs j inputs
38
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
<
≤≤−−
≤≤−−
<
=
xc
cxbcbcx
bxaabax
ax
cbax
0
0
),,,(µ (2.57)
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
<
≤≤−−
<<
≤≤−−
<
=
xd
dxcdcdx
cxb
bxaabax
ax
dcbax
0
1
0
),,,,(µ (2.58)
)2ln(2
),,(⎟⎠⎞
⎜⎝⎛ −
−= w
px
ewpxµ (2.59)
The rule base with r rules is given by:
∏==
j
i imr1
, (2.60)
can be described as follows:
44 344 2144 344 21econsequencantecedent
z npropositionpropositioR ><>< THENIF: (2.61)
where z is rule number, rz ≤≤1 .
For option of fuzzy antecedent – fuzzy consequence the rule can be expressed
as follows:
Rz : IF x1 is zA1 AND … xk is zkA THEN y is Bz (2.62)
For fuzzy antecedent – crisp consequence the equation is:
39
Rz : IF x1 is zA1 AND … xk is zkA THEN z
Tz cxy +=η , (2.63)
],,,[ 21 zjzzTz ηηηη K=
In the fuzzy system each rule mentioned above is basically evaluated using
Generalized Modus Ponens (GMP) inference, i.e.:
Premise : IF x is A THEN y is B
Antecedent : x is A′
Consequence : y is B′
Commonly, this evaluation result, zβ , can be implicated in two options, i.e.:
)( and )( and )()( 21
1 21 jzA
zA
j
i
zAi
zAz xxxx
jjµµµµβ L∏
=
== (2.64)
or
)( and )( and )())((min 21 21 jzA
zA
zAi
zAiz xxxx
jjµµµµβ L== (2.65)
where Equation (2.64) is often called product implication, while Equation (2.65) is
minimum implication. In design, the rule’s consequences aggregation can also be
defined in two ways, i.e. weighted and maximum as described as follows:
Vy
yyyyy B
r
iBBBB ir
∈∀
== ′=
′′′′ ∑
)()()(or )(or )(1
21µµµµµ L
(2.66)
or
Vy
yyyyy BBiBBB ir
∈∀
== ′′′′′
)())((max)(or )(or )(21
µµµµµ L (2.67)
where )(yzB′µ as the inference engine operator can be selected from type of Mamdani
fuzzy consequence or Larsen fuzzy consequence (Olivares, 2003), i.e.:
40
Vy yy zBB zz∈∀=′ )),(min()( βµµ (2.68)
or
Vy yy zBB zz∈∀=′ )()( βµµ (2.69)
Finally, this section also presents a brief review of the last step of operation in
a fuzzy system, i.e. defuzzification. It has two options, i.e. centre of gravity and mean
of maxima. The center of gravity has mathematical expression as follows,
∫∫
∈ ′
∈ ′=
Vy B
Vy B
dyy
ydyyy
)(
)(0 µ
µ (2.70)
while the mean of maxima is:
∫∫
=)'(
)'(0
Bhgt
Bhgt
dy
ydyy (2.71)
where
))((maxarg)'( ' yBhgt BVy
µ∈
= . (2.72)
For direct crisp output of crisp rule’s consequences aggregation the weighted
average y0 can be described as:
∑∑
=
=+
= r
i i
r
i iTii cx
y1
1 00
)(
β
ηβ (2.73)
From the options described in Equations (2.57) to (2.73) the most used fuzzy
systems in system engineering and control, namely the Mamdani type and Takagi-
Sugeno type can be characterized as follows: Mamdani fuzzy system has minimum
implication, membership functions as consequence, maximum aggregation, and
41
centre of gravity defuzzifier, while the Takagi-Sugeno type has product implication,
linear input function as consequence, and weighted average aggregation defuzzifier.
This section shall adequately presents a brief review of fuzzy systems. However, the
quality of a fuzzy controller design does not merely depend on the types or options
selected, but it is implied by how the controller should be properly set to meet with
the system being controlled.
2.7 Knowledge Based Fuzzy Control
The term ‘knowledge-based fuzzy control’ was clearly first quoted in Rhee et
al. (1990). The term consists of two components, i.e. knowledge-based system
(KBS) and fuzzy control. These two parts can be deducted as systems or methods
that employ expertise of human to derive its explanations, procedures, algorithms
and its concluded rules that will be applied. In other descriptions, systems that the
controls are influenced with human expertise can be considered as expert system.
Expert system is a term used to represent a ‘method of control’ that mainly based on
the human expertise (the knowledge of the expert) whether directly or indirectly.
Directly means the knowledge of the expert is supplied to the system online, and
indirectly means the knowledge is reprocessed as rules.
Ignizio (1991) defined expert system as a computer program (or methods of
computation) that exhibits, within a specific domain, a degree of expertise in
problem solving that is comparable to that of human expert. These expert systems
follow the concept of Model-Based Reasoning that the model contains an explicit
description of a domain, objects, relationship between objects, and taxonomy of the
object classes, Soucek (1989). In contrast, fuzzy logic control that initiated by Zadeh
basically has inherent problems on reasoning in designing rules. Ordinary fuzzy
control has no adaptation algorithm to reorganize the rules when system is running in
which the common way to design the proper rules are usually heuristically approach.
To solve the problem, several researchers intensively investigated techniques in order
how to make fuzzy control online and having adaptation capability, such as Jang
42
(1993), Mar and Lin (2001), and Hassanzadeh et al. (2002). If the online adaptive
fuzzy control is not a simple way to be implemented in certain control system case,
optimizing the fuzzy rules thru knowledge-based reasoning can be a considerably
choice.
Rhee et al. (1990) rigorously described how to implement a knowledge-based
fuzzy logic in control systems. They investigated a method for fuzzy control of
system based on a concept of human thinking. Their fuzzy controller consists of a
knowledge-based containing a number of process time responses. The basic elements
employed were cells in which an input and corresponding output of system were
stored. The cells were organized according to different types of relations that the
result was defined as knowledge structure. They distinguished the control design in
two phases. The former is learning process (knowledge investigation and
representation) in which the relations between input and corresponding output are
investigated. In this phase the knowledge structure is constructed. Then, the latter
phase is implementation of the knowledge structure to control the process. In the
research project a similar way of knowledge-based fuzzy (KBF) control incorporated
to AFC scheme is proposed in order to design a robust motion control of mobile
manipulator. The application of the knowledge-based fuzzy logic mentioned above to
feedback controls is rarely found in literatures. Most of the implementations are in
data retrieval and image segmentation/processing that is very useful in medical
diagnosis system.
An investigation on knowledge-based fuzzy logic method that used genetic
algorithm to refine the knowledge representation and acquisition can be seen in
Ouchi and Tazaki (1998). They used a fuzzy petri-net to perform fuzzy reasoning.
However their method was applied to medical diagnosis system and it should be
combined with a feedback control to perform the use in engineering field such like
robotics. Nanayakkara and Samarabandu, (2003) implemented a class of knowledge-
based fuzzy logic to automatic model-based image segmentation system in medical
diagnosis system. They successfully showed the implementation on ultrasound image
of prostate.
43
2.7.1 Knowledge Based Reasoning in Fuzzy System
As mentioned previously, a fuzzy system attempts to mimic human experts’
knowledge. This means the building of a fuzzy system can be considered as a fuzzy
expert system. A good fuzzy system should include all of the human expertise
aspects into the design. However, in a procedural fuzzy system design there is still
classical problems in reasoning. Theoretically there is no specific reasoning guidance
to design, for example, what are the best of membership of functions and its
configuration. Basically, reasoning in fuzzy system or fuzzy expert system design
can be achieved through two ways, i.e. forward chaining and backward chaining
inference engine (Negnevitsky, 2002). This follows the basic reasoning of rule-base
expert systems as well as for fuzzy expert systems. If an expert (human) first needs
to gather some information and then tries to infer from it whatever can be inferred,
the forward chaining inference engine is the choice. In contrast, if the expert begins
with a hypothetical solution and then attempts to find facts to prove it, the backward
chaining inference engine is the suitable choice. One of the proposed methods in this
study, i.e. Knowledge Based Fuzzy Active Force Control, uses a method that similar
with the backward chaining inference engine in the design. A typical process in
developing the fuzzy expert system with backward chaining inference engine
approach (Negnevitsky, 2002), incorporates the following steps:
a) Specify the problem and followed by defining linguistic variables.
b) Determine fuzzy sets.
c) Elicit and construct fuzzy rules.
d) Encode the fuzzy sets, fuzzy rules and procedures to perform fuzzy
inference.
e) Evaluate and tune the system.
In a backward chaining approach the steps mentioned above can be modified
as follows:
a) Specify the problem.
b) Investigated the relation of the input and output functions.
44
c) Defining linguistic variables.
d) Elicit and construct fuzzy rules.
e) Encode the fuzzy sets, fuzzy rules and procedures to perform fuzzy
inference.
f) Evaluate and tune the system.
A latest example of an application of knowledge-based fuzzy control can be
found in Ciliz (2005). His contribution is about tuning algorithm and rule-base
reduction through knowledge-based investigation. He proposed an algorithm that
computed the inconsistencies and redundancies in the overall rule set based on newly
proposed measure of equality of the individual fuzzy sets. He reported that the
algorithm was successfully tested experimentally for the control of a commercial
household vacuum cleaner.
2.8 Motion Planning
In past two decades, the motion planning problems have been extensively
studied and it is in fact one of the better-formulated problems in robotic study.
Generally motion planning transforms the high-level mobile robot’s commands into
a sequence of low-level motor actuating signals. Through motion planning, the robot
user is able to specify the desired high-level activity with the system itself that fills in
the missing low-level details (Sharir, 1989). Motion planning of the mobile robot
involves various subfields and disciplines, such as path planning and trajectory
planning.
2.8.1 Path Planning
One of the main aspects in motion planning is the path planning which
addresses the geometric concerns of robot motion without regard to time. There are
two stages involved in path planning, i.e global path planning and local path
45
planning. For global path planning, the robot system’s geometry is fixed to either a
circle or polygon, while the environment can be arbitrary. However, for local path
planning, instead of fixing the robot system’s geometry, the operating environment
of the robot is fixed. In this project, only global path planning is considered.
Generally, path planning can be solved by two approaches, they are model-based
path planning and sensor-based path planning.
2.8.2 Trajectory Planning
Trajectory planning concerns with the time history of a series of the collision-
free configurations which are obtained through path planning (Aydin and Temeltas,
2002). In this case, trajectory planning is actually an interface between the motion
planner with the motion controller. Trajectory planning obtains the time-independent
geometry points from the path planner and at the same time instills the time element
into the planned path to transform it into the time-indexed trajectory. Several
approaches have been introduced in past few years for the formulation of the
trajectory planner.
Zulli et al. (1995) had proposed an interface between the motion planner with
the motion controller. The interface transformed the output of the motion planner
which was presented as a sequence of arcs and segments, into a time-indexed
trajectory. Later, Hu et al. (1997) introduced the hybrid control architecture for the
mobile robot motion planning. An intelligent expert system was constructed for the
selection of the best motion command from the motion planner which was then fed
into the motion controller.
Piazzi and Guarino (2000) proposed the Quintic G2-splines for the trajectory
planning of the mobile robot. Quintic G2-spline interpolates an arbitrary sequence of
points with overall second order geometric continuity.
46
2.9 Virtual Reality (VR)
With the advent of the first model drawing, design, and construction by the
aids of the computer, the next logical step will be the use of virtual reality (VR). VR
is based on a model of reality where the computerized information is represented as a
separate, two or three-dimensional object in the computer and it can be experienced
directly and interactively by the participant to provide him a sense that he is inside
the data space (Schmitt, 1993). Broadly, there are three forms of VR, typically
referred to as desktop VR, projection VR, and immersive VR.
Desktop VR resorts to a range of computing equipments, from personal
computers to powerful graphics workstation in order to enable the participant to
build and interact with the virtual worlds. Meanwhile, projection VR differs from
desktop VR in the sense that it polarizes the computerized graphical images from a
pair of conventional video projectors to provide groups of individuals a large-screen
stereoscopic graphic (Stone, 1995). Immersive VR is more to the description of the
participant’s experience of “being there” in the virtual environment through VR
interaction tools, such as the head-mounted displays and interactive gloves. In this
project, the developed VR wheeled mobile robot simulator is based on the concept of
desktop VR.
The principles of VR are immersion and interactivity. Immersion is achieved
through blocking out all sorts of distractions from the participant so that he can focus
selectively on just the information which he wants to work with. Interactivity means
the ability for the participant to interact with the events in the virtual world (Zheng,
et al., 1998). Generally, a VR system should consist of three aspects that should be
taken into account. It should be able to response to participants or users actions,
provide real-time 3D graphics and instill a sense of immersion into the participants
vision. Since VR is still considered by many as relatively an embryonic technology,
it’s potentials are largely open-ended.
47
2.10 Conclusion
A number of theories, fundamental concepts and relevant literature related to
the research have been highlighted in this chapter. These shall serve as the basis to
design a number of robust AFC-based systems effectively since the AFC part relies
heavily on the appropriate technique to estimate the real-time inertia matrix in the
AFC feed forward control loop of the mobile manipulator. From the study, it is
feasible to improve the robot control scheme by implementing an intelligent method
like fuzzy logic or knowledge-based system due to the complexity and the non-linear
aspects of the system and its environment. A deeper understanding of the mobile
robot’s interaction with the environment can be explored by means of a virtual reality
(VR) technique embedded with the motion planning and control. All the essential
elements described in this chapter shall be suitably employed in the proposed control
schemes which will be duly described in succeeding chapters.
CHAPTER 3
ESTIMATION OF INERTIA MATRIX BASED ON
ωv -ACTIVE FORCE CONTROL WITH FUZZY LOGIC
3.1 Introduction
In this chapter, an inertia matrix estimation method using fuzzy logic (FL) for
an AFC scheme is presented. Generally, the inertia matrix of a mobile robot is not
fixed, but it is changing with the motions of the mobile robot. Therefore, in relation
to the changes of the mobile robot motions, the estimated inertia matrix IN should be
approximately adapted for maximum performance of the mobile robot. The aim of
this chapter is to improve the inertia matrix estimation method by switching the usage
of crude approximation method to the proposed FL method. The FL mechanism
computes IN automatically and continuously, while the mobile robot is tracking the
reference trajectory. Finally, the performance of the proposed ωv -AFC-FL control
method is compared to the previous ωv -AFC control scheme which has adopted the
crude approximation technique in the estimation of IN.
3.2 Fuzzy Logic Applied to Robotics
Recently, some researchers have investigated the application of FL in the
control of mobile robot. A number of fuzzy controllers are developed for steering
control, as proposed by Hu and Yang (2003) as well as Antonelli et al. (2002). Some
49
of the others are used for the navigation control of mobile robot in the unknown
working environment, with the presence of obstacles. For obstacles avoidance, the
mobile robot should be equipped with sensors such as camera, sonar or infrared
sensing devices. Sensors detect the existence of the obstacles and the location of the
object in the workspace. In Aycard et al. (1997), actual orientation error or velocity is
used as the inputs for the fuzzy membership function, while the outputs are velocity
and heading angle. The difficulties of fuzzy design lie in the choice of appropriate
inputs for fuzzification, the rules definition and defuzzification outputs (Aycard et al.,
1997).
Mailah and Rahim (2000) have investigated a method for the estimation of
inertia matrix for a robot arm, which is controlled by the active force control strategy
(AFC) with embedded fuzzy logic mechanism. Fuzzy logic is incorporated into the
control scheme to compute the inertia matrix (IN) of a robot arm intelligently, so that
it can be utilized by the AFC mechanism in disturbance compensation. The inputs for
the fuzzy membership function are the vector of joint angles ),( 21 θθ , while the
outputs are the elements of the estimated inertia matrix ),( 21 ININ , for the first and
second arm, respectively.
In this study, FL is applied to the system in order to obtain the ‘optimal’
values of the estimated inertia matrix similar to a study by Mailah and Rahim (2000).
However, the inputs for the membership function in this mobile robot research are
different from those described in their work. There are several potential variables that
can be used as the input for fuzzy controller, namely linear and angular velocities, left
and right wheel accelerations, trajectory tracking errors and the heading angle.
3.3 Fuzzy Logic Design
Mamdani method is widely accepted for expert knowledge capturing. It
allows us to describe the expertise in more intuitive, more human-like manner.
However, Mamdani-type fuzzy inference entails a substantial computational burden.
On the other hand, Sugeno method is computationally effective and works well with
50
optimization and adaptive techniques, which makes it very attractive in control
problems, particularly for dynamic nonlinear systems.
3.3.1 Definition of the Linguistic Variables
First of all, the inputs and outputs of the fuzzy controller system need to be
identified. There are several potential variables as inputs the proposed fuzzy
controller, namely acceleration, linear velocity, linear and angular velocities,
trajectory tracking errors, heading angle and the estimated inertia matrix, IN as
output. Figure 3.1 illustrates the configuration of the inputs and outputs of a fuzzy
controller.
Inputs Outputs
Figure 3.1: Inputs and outputs of the fuzzy controller
Figure 3.2 shows the comparison of trajectory tracking errors of the mobile
robot considering different fuzzy inputs, namely acceleration and linear velocity,
linear and angular velocities and trajectory tracking error and heading angle. These
were tried on a control scheme to determine which combination produces the
minimum error. It is observed that by using acceleration, linear velocity as the input
variable for the fuzzy controller, the trajectory tracking error is the minimum.
Therefore, in this study, the acceleration and linear velocity combination is chosen as
the inputs for the fuzzy controller. The input linguistic variables are shown in Tables
3.1 and 3.2.
Fuzzy
Controller
51
Figure 3.2: Comparison of trajectory tracking error using various inputs
Table 3.1: Acceleration
Linguistic Variable: Acceleration
Linguistic Value Numerical Range
Very Low (VL) -2.0 to 0.0
Low (L) -1.0 to 1.0
Medium (M) 0.0 to 2.0
High (H) 1.0 to 3.0
Very High (VH) 2.0 to 4.0
Table 3.2: Linear velocity
Linguistic Variable: Linear Velocity
Linguistic Value Numerical Range
Very Slow (VS) -0.1 to 0.3
Slow (S) 0.1 to 0.5
Medium (M) 0.3 to 0.7
Fast (F) 0.5 to 0.9
Very Fast (VF) 0.7 to 1.1
52
For IN, it is classified into following sets: very small (VS), small (S), medium
(M), big (B) and very big (VB). The output linguistic variables are as shown in Table
3.3.
Table 3.3: Estimated inertia matrix, IN
Linguistic Variable: IN
Linguistic Value Numerical Range
Very Small (VS) -0.1 to 0.3
Small (S) 0.1 to 0.5
Medium (M) 0.3 to 0.7
Big (B) 0.5 to 0.9
Very Big (VB) 0.7 to 1.1
3.3.2 Determination of Fuzzy Set
There are various shapes of fuzzy set, but usually only triangle or trapezoid is
chosen as the fuzzy sets, since it provides an adequate representation of the expert
knowledge and at the same time it is simplifies significantly the computation
prepossesses. The linguistic variables of inputs are presented in Figures 3.3(a) and
(b), while the output membership function is shown in Figure 3.4.
(a) Acceleration (b) Linear velocity
Figure 3.3: Inputs functions
53
Figure 3.4: Estimated inertia matrix as the output function
3.3.3 Design of the Fuzzy Rules
To design the fuzzy rules, the knowledge or information about the behaviour
of the relevant part of the proposed systems should be first obtained and later
described in the form of fuzzy linguistic variables. The required knowledge for the
design of the rules (solutions) can be gathered from other relevant sources such as
books, computer databases, results from previous studies and observed human
behaviour.
For FL method, the output range of the estimated inertia matrix is set from
0.1 to 0.9 kgm2. Using a heuristic method, if the acceleration and the velocity are
high or fast, the estimated inertia matrix of the dynamic system should be relatively
high. On the contrary, if the acceleration and the velocity are low or slow, estimated
inertia matrix of the dynamic system should be low. Therefore, the fuzzy rules can be
created as shown in Figure 3.5.
54
Acceleration
Figure 3.5: Fuzzy rules
The new output membership function is shown in Figure 3.6.
Figure 3.6: Extended estimated inertia matrix
In this research, there are two inputs and one output. In order to link the
fuzzified inputs with the output, 55× fuzzy rules have been developed as follows:
1. If (Linear Velocity is Very Slow) and (Acc. is Very Low) then (IN is Very Small)
2. If (Linear Velocity is Very Slow) and (Acc. is Low) then (IN is Very Small)
3. If (Linear Velocity is Very Slow) and (Acc. is Medium) then (IN is Small)
4. If (Linear Velocity is Very Slow) and (Acc. is High) then (IN is Small)
0.5VH
0.4
0.3
0.2
0.1
F M
S VSS
0.6
0.5
0.4
0.3
0.2
0.7
0.6
0.5
0.4
0.3
0.8
0.7
0.6
0.5
0.4
0.9
0.8
0.7
0.6
0.5
VL L M H VH
55
5. If (Linear Velocity is Very Slow) and (Acc. is Very High) then (IN is Medium)
6. If (Linear Velocity is Slow) and (Acc. is Very Low) then (IN is Very Small)
•
•
•
25. If (Linear Velocity is Fast) and (Acc. is Very High) then (IN is Very Big)
In this research, FL controller is developed using the Fuzzy Logic Toolbox®
to be used with MATLAB and Simulink. The rule editor, surface viewer and rule
viewer as shown in Figures 3.7 and 3.8 have been utilized for the determination of the
characteristics of the proposed fuzzy controller.
(a) Rule editor (b) Surface viewer
Figure 3.7: Rule editor and surface viewer
Figure 3.8: Rules viewer
56
3.4 Simulation
The simulation work is performed using the MATLAB/Simulink software
packages. The block diagram for the ωv -AFC-FL is shown in Figure 3.9. Compared
with the previous control scheme, namely ωv -AFC, ωv -AFC-FL has been
incorporated with FL algorithm which is mainly applied for the estimation of IN.
Figure 3.9: Simulink block diagram of ωv -AFC-FL
3.5 Results and Discussion
Simulation in this chapter is different with the previous simulation since it
considers only quarter of desired circular trajectory. This is due to that the fact, the
significant instability occurs only at the starting condition. Hereafter, the trajectory
tracking error experiences minor changes only. Therefore the analysis will focus on
the starting condition only.
Simulation studies on ωv -AFC-FL controller are conducted in the existence
of various disturbances, namely the trajectory tracking errors generated by ωv -AFC
controllers are then compared with ωv controller as shown in Figures 3.10 (a) to (d).
57
(a) oF (b) dT
(c) sF (d) kF
(e) fF (f) hF
Figure 3.10: Comparison of the trajectory tracking errors in various disturbances
Figures 3.10 (a) to (f) show that the trajectory tracking error for ωv controller
is generally very large, whilst those of ωv -AFC and ωv -AFC-FL schemes are much
58
smaller. Therefore, it is obvious that with the incorporation of AFC into the robotic
system, the accuracy and stability of the system is greatly enhanced. Figures 3.11 (a)
to (f) illustrate the comparison of results between ωv -AFC and ωv -AFC-FL in
greater details.
(a) oF (b) dT
(c) kF (d) sF
(e) fF (f) sF
Figure 3.11: Comparison of the trajectory tracking errors between ωv -AFC and ωv -AFC-FL schemes
59
From Figure 3.11, it is observed that the trajectory tracking error for ωv -AFC is
generally very coarse and rugged, while the trajectory tracking error for ωv -AFC-FL
is relatively stable in smooth. It is clear that the ωv -AFC-FL is more capable and
smooth in the estimation of IN compared with ωv -AFC.
3.6 Conclusion
The proposed ωv -AFC-FL scheme has been developed, simulated and
applied to the mobile robot. It performs excellently even under the influence of
external disturbances. The FL mechanism computes IN automatically and
continuously while the mobile robot is in operation. The main advantage of obtaining
the estimated inertia matrix using FL is that it causes the fluctuation of the tracking
error to considerably decrease compared to the crude approximation method showing
that the AFC scheme is able to make the system robust and stable. The FL
mechanism manages to compute IN automatically and continuously, while the mobile
robot is commanded to track the referenced trajectory by driving the motor (and
hence the robot) smoothly to the desired positions.
CHAPTER 4
VIRTUAL WHEELED MOBILE ROBOT SIMULATOR
4.1 Introduction
In this chapter, a virtual reality (VR) method is introduced and applied to the
motion planning and control of a wheeled mobile robot (WMR). Research on the
integration of VR with robotics is relatively new. Sensing the potentials of VR in
robotics, a new era of research that is primarily concerned with the construction of
the virtual simulator for robotic experimentation has evolved. In the simulator, the
VR provides an advanced human-computer interface and this has greatly facilitated
the study of robotics. In this chapter, the integration of VR into the simulation of the
WMR will be discussed appropriately. The first section of the chapter touches on a
description of the robot simulator and highlights the overall architecture of the
proposed virtual WMR simulator. This is followed by the construction of the scene
graph for the virtual environment (VE) of the mobile robot’s workspace (layout). In
addition, the elements within the scene graph will be also briefly discussed. The
simulation study based on some of the theoretical concepts and principles derived
from previous chapters are fully described in this chapter. Collision avoidance of
obstacles is also discussed in the chapter based on a selected algorithm. The overall
system is tested and evaluated considering the WMR to operate in a computer
integrated manufacturing (CIM) environment.
61
4.2 Robot Simulator
For the experimentation of robotics, it is not necessary to have a physical
robot and thus the hardware of the robot is actually incidental in this case (Schildt,
1987). In fact, it is the software that differentiates a robot from a machine. A robot
simulator actually provides an imaginary world for the testing of the robot control
algorithms. In general, a robot simulator should be instilled with the robotic-control
algorithms, a database to store spatial information about the workspace, and a
complete display of the motion-simulation results. In this research, the constructed
virtual WMR simulator is equipped with the capabilities in path planning and motion
control. Meanwhile, for the presentation of the simulation results, a specific VR
technique has been applied in order to improve the analysis of the results. The overall
architecture of the virtual WMR simulator is discussed in the following sections.
4.3 Overall Architecture of Virtual WMR Simulator
The construction of the virtual WMR simulator involves the aspects of
motion path planning, motion control and the application of VR technique. Therefore,
in order to ensure a systematic and effective simulation study to be carried out, the
coordination and inter-relationship between all these subfields have to be carefully
planned and implemented. The integration of all these fields of study for the
construction of the virtual WMR simulator is as shown in Figure 4.1. A block
diagram showing the interaction of the main components of the proposed simulator is
illustrated in Figure 4.2.
At first, the map of the workspace for the virtual mobile robot is captured by
a virtual camera that is installed within the virtual environment. The map
(represented in bitmap form) is then interpreted and analyzed for the generation of
the configuration space and the six elementary jumps graph. From this generated six
elementary jumps graph, the path planner searches for a near-optimal time-
independent collision-free path through A* heuristic search algorithm which is
highlighted in Appendix A. Since the motion control algorithm requires the input of
62
the time-based reference trajectory, this geometrically planned collision-free path has
to be transformed into a function of time. For this purpose, the concept of parametric
cubic spline interpolation has been applied for the modelling of the trajectory planner.
Figure 4.1: Interlinking of motion planning, motion control and VR
Considering the planned trajectory as the reference trajectory where the
mobile robot is required to replicate (converge), the errors of the motion can be
obtained through the subtraction of the reference states (qref , and refq& ) from the
actual states (qact, and actq& ) of the mobile robot. The errors are then fed forward into
the resolved acceleration control (RAC) component for the generation of the
acceleration commands, cq&& . Since the total DOF of the WMR is three, while
controllable DOF is two, therefore the DOF for cq&& has to be stepped down to two.
63
The transformation of cq&& into the right and left wheel acceleration lr ,θ&& is as
described in Chapter 2.
Figure 4.2: A block diagram of the virtual WMR simulator
From the calculated lr ,θ&& together with the disturbance torque, τd and actual
acceleration, actq&& , the active force control (AFC) will generate the control torques for
the right and left motors of the mobile robot which will be fed into the WMR
dynamic model as the actuating torques. The corresponding motions of the mobile
robot are then integrated for the estimation of qact and actq& . Meanwhile, the geometry
of the WMR within the virtual environment will also be transformed according to the
current states, qact of the mobile robot. Finally, qact and actq& are fed back for control
purposes.
4.4 Trajectory Planning
The path planner generates only a geometrical collision-free path and it is not
ready for use by the motion controller which requires the time-based trajectory
parameter as the input. Therefore, the geometrical collision-free path has to be
64
redefined into a time-based trajectory before it is fed into the motion controller for
the trajectory tracking control. For this purpose, a trajectory planner has to be
modelled in such a way that it is able to approximate the desired shape of the path
curves into functions of time. Meanwhile the generated trajectory functions should
also use less memory resource and able to offer easier manipulation of the collision-
free path.
It is assumed that the geometrical collision-free path is actually a sequence of
points in three dimensions (x, y,φ) through which the mobile robot is required to
follow. In this research, the parametric cubic spline functions are applied for the
description of the trajectory functions. This is because the parametric representation
of curves in the form x=x(t), y=y(t), φ=φ(t), is able to overcome the problems caused
by the functional or implicit forms. Polynomials which are of lower-degree than
cubic polynomials provide too little flexibility in controlling the shape of the path,
while higher-degree polynomials can introduce unwanted ‘wiggles’ and also require
more computational resources (Foley et. al, 1996). The general form of the
parametric cubic spline function is given as
Q(t) = a1 t3 + a2 t2 +a3 t +a4 (4.1)
With reference to equation (4.1), the parametric cubic polynomials that define
a segment of the path, Q(t) = [x(t) y(t) φ(t)] are as follows:
x(t) = a1x t3 + a2x t2 + a3x t + a4x ,
y(t) = a1y t3 + a2y t2 + a3y t + a4y ,
φ(t) = a1φ t3 + a2φ t2 + a3φ t + a4φ , 0 ≤ t ≤ 1. (4.2)
By considering q(tk) = qtk , and q ’(tk) = q ’tk and k is the number of segments
of the curve, the coefficients, a1 , a2 , a3 , and a4 in Equation (4.1) can be expressed
as (Cook and Ho, 1985):
65
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−−−
−
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+
+
++++
++++
1
1
112
12
1
21
21
31
31
4
3
2
1
''
00010100
1233
1122
k
k
k
k
kkkk
kkkk
qqqq
tttt
tttt
aaaa
(4.3)
From Equation (4.3), q ’ has to be calculated first before the coefficients a1,
a2, a3 , and a4 for each curve segment can be obtained. For the computer-controlled
WMR, it is assumed that the initial and goal states of the mobile robot are zero.
Therefore, through a geometrical path with n points, this standstill condition
produces the boundary conditions,
q ’1 = q ”1 = q ’n = q ”n = 0 (4.4)
Meanwhile, through the assumption of the continuity constraints between
neighbouring spline segments as follows:
q ”(tk+1) = q ”(tk) (4.5)
The calculation of q’ is given as:
[Mat] [q ’] = [Ar] (4.6)
where,
( )( )
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+
⋅⋅
++
+
=
−−
++++
nnn
kkkk
ttt
tttttttt
ttt
Mat
321
22
132
11
1122
3344
323
66
( ) ( )
( ) ( )[ ]
( ) ( )[ ]
( ) ( )⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−+−
⋅⋅
−+−
−+−
−+−
=
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
⋅⋅
=
−−−−
+++++++
−
+
122121
12
2122
121
232434
23
43
1222
2323
1
1
3
2
63
3
3
63
,
'
'''
'
nnn
nnn
kkkkkkkk
r
n
k
qqt
qqt
qqtqqttt
qqtqqttt
qqt
qqt
A
q
qqq
q (4.7)
By taking the tri-diagonal characters of the coefficient matrix [Mat], the
solution of Equation (4.6) can be obtained through Gaussian elimination to yield [q ’]
which is then used for the calculation of the coefficients a1, a2, a3, and a4 in Equation
(4.3). The velocity and acceleration of the mobile robot can be obtained through the
respective first and second derivatives of Equation (4.1) as follows:
q ’(t) = 3a1 t2 + 2a2 t + a3 (4.8)
q ”(t) = 6a1 t + 2a2 (4.9)
4.5 Scene Graph of Virtual Environment
Virtual environment (VE) is actually composed of various objects, such as
the lights, positional information, fogs and geometries. In order to manage all these
objects systematically, the concept of scene graph is applied, where the whole
structure of VE is maintained in a hierarchical structure (Engineering Animation,
1999) as shown in Figure 4.3. The actual scene graph program of the virtual
environment for the CIM facility is shown in Appendix B.
This kind of structure resembles an upside-down tree since the root is at the
top, and the branches and leaves are at the bottom. With reference to Figure 4.3, the
Root Node is the ancestor for all other Nodes. The Root Node has several Child
Nodes which are the direct descendant of it, such as the Light Node and Group Node.
67
Parent Node is defined as a Node’s direct ancestor, and every Child Nodes is allowed
to have only one Parent Node. For example, at the second level of the hierarchical
tree, the Content Node, and both of the Separator Nodes only have one single parent,
that’s the Group Node.
Figure 4.3: Hierarchical structure of the scene graph for a VE
Generally, all the objects in the virtual environment are represented as Node,
which is the most fundamental element of the scene graph. The Node contains the
information about the physical objects, and it can be categorized into Content Node
and Grouping Node. Content Node holds the information about the VE and there are
generally four types of Content Nodes: Geometry Node, Light Node, Transform Node,
and Fog Node. Geometry Node contains the geometrical information about the
physical and spatial states of an object. Meanwhile, the Light Node describes the
lighting conditions of the virtual environment in terms of the light’s position,
intensity, ambient colour, and diffuse colour. On the other hand, the Fog Node holds
the information about the characteristics of the fog within the VE. The fog is a
special effect that simulates environmental conditions such as smoke, haze, and mist
68
which will obscure the view ability within the VE. The Transform Node contains the
position or spatial transformation of the specified objects.
Unlike the Content Node, Grouping Node does not hold any direct
information about the VE. However the presence of Grouping Node is essential in
maintaining the hierarchical structure of the scene graph. Basically there are two
types of Grouping Node: Organizational Node and Procedural Node. The main
function of the Organizational Node is to group and encapsulate a set of Nodes in
order to share the same common states together. The Organizational Node consists
of Group Node, Separator Node and Transform Separator Node. Procedural Node
acts in the same way as the Organizational Node but it contains additional
information for the actuation of only one child node while deactivating the others.
The Procedural Node consists of Level-Of-Detail (LOD) Node and Switch Node.
In the scene rendering, WorldToolKit (WTK) begins with the Root Node
which is the entry point into the scene graph, and this is followed by all the Nodes
attached to it from top to bottom and left to right order. When WTK encounters a
Node with more than one Child, the first child’s branch will be explored until all the
Child Nodes within this specified Node is traversed completely. Figure 4.4 illustrates
the procedures of VE rendering of the scene graph in Figure 4.3.
69
Figure 4.4: Procedures of VE rendering for a hierarchical structured scene graph
4.6 Simulation Setup
The virtual WMR simulator is constructed using Microsoft Visual C++ aided
by the programming-ready mathematical functions that are provided by the
MATLAB library. Besides, the incorporation of WTK has also reduced the
programming burden in the construction of VE. For ease of program handling, the
concept of object-oriented programming has been adopted in the study.
During the simulation, the WMR is required to plan or opt for a collision-free
path which is then transformed into a time-based reference trajectory. The obtained
reference trajectory is fed into the motion controller algorithm for the mobile robot
trajectory tracking control. Meanwhile, the WMR is perturbed from its reference
trajectory by the constant disturbance torques and the harmonic disturbance torques
for the testing of the system’s robustness and stability. The simulation results are
finally used for the motion transformation of the virtual robot within the VE. A
70
number of assumptions, parameters and techniques used in the study have been made
and chosen for the construction of the virtual WMR simulator. They are described
accordingly as follows:
a) Nonholonomic Motion Planning
Mobile robot perception sensors: Assumed perfect models
Search space applied: 6-elementary jumps graph
Graph searching method: A* heuristic search
Trajectory planning method: Parametric cubic spline
interpolation
b) Initial and Final Conditions of WMR
Initial configuration of WMR:
0.00.0
713.40.8000.100
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
=
li
ri
i
i
i
i
yx
q
θθφ
Goal points: (1350,700)
Goal orientation: Unspecified
c) WMR Parameters:
Driving wheel radius: r = 0.15 m
Distance between wheels and
axis of symmetry: b = 0.75 m
Distance between Po and Pc: d = 0.03 m
Mass of vehicle: m = 31.0 kg
Mass of platform: mc = 30.0 kg
Moment of inertia of vehicle: I = 15.625 kgm2
Moment of inertia of wheel: Iw = 0.005 kgm2
d) RAC Parameters:
Proportional constant for ex: Kpx = 200.0
Proportional constant for ey: Kpy = 200.0
Proportional constant for eφ: Kpφ = 200.0
71
Derivative constant for ėx: Kdx = 30.0
Derivative constant for ėy: Kdy = 30.0
Derivative constant for ėφ: Kdφ = 30.0
e) Active Force Control Parameters
Motor constant: ⎥⎦
⎤⎢⎣
⎡=
263.0263.0
tK Nm/A
AFC constant: ⎥⎦
⎤⎢⎣
⎡=
0.10.1
cK
Crude approximation of inertia
matrix: IN ⎥⎦
⎤⎢⎣
⎡=
2.02.0
kgm2
f) Applied Disturbances
Constant disturbance torque: τa = [3 3] Nm
Harmonic disturbance torque
(right wheel): τhr = 3sin(0.5t)+3 Nm
Harmonic disturbance torque
(left wheel): τhl = 3sin(0.5t+π/2)+3 Nm
g) Simulation Parameters for Collision-Free Trajectory Tracking
Tangential velocity: Vel = 0.5 m/s
Integration algorithm: ode45 (Dormand-Prince)
Simulation time steps: 0.1 s (not in real-time)
Before the actual execution of the simulation program, a heuristic method is
applied for the estimation of the controller gains, Kpx, Kpy, Kpφ, Kdx, Kdy, and Kdφ,. The
obtained values of these gains are assumed to be suitable for the purpose of
simulation study. The AFC constant, Kc is set to 1.0 for full AFC implementation.
The constructed virtual WMR simulator requires tighter control of some of the more
important parameters in order to ensure a more robust and precise operation of the
robotic system within the VE. Initially, the virtual simulation is performed in an ideal
72
workspace without considering any disturbances. At a later stage, disturbances are
modelled and applied to the system to test the robustness of the simulator.
4.7 Simulation Results and Discussion
Through the constructed virtual WMR simulator, the mobile robot has been
experimented under three different kinds of loading conditions. At first the mobile
robot is assumed to be working in an ideal workspace where it is free from all sorts
of disturbances. Later, the mobile robot is exposed to the constant and harmonic
disturbance torques individually. During simulation, the results for each simulation
task are obtained, analysed and compared.
Figure 4.5 (a) illustrates the trajectory tracking of the virtual WMR which is
free from disturbances. Figure 4.5 (b) and (c) show the trajectory tracking activities
of the virtual WMR under the disturbances of τa and τh respectively. From these
three graphs, it is obvious that the mobile robot is fully capable of planning for a
global collision-free path which will then be used for the trajectory tracking purposes.
With the incorporation of AFC scheme into the motion controller, the robustness of
the robotic system has been greatly enhanced. The AFC scheme has successfully
generated the compensation torques used for disturbance cancellation, provided that
the estimated inertia matrix has been appropriately obtained.
With reference to Figures 4.5 (d) to (f), the track errors as well as the
orientation errors for the virtual WMR are generally small and this small margin of
errors has successfully kept the virtual WMR on track. However, it is obvious that
the performance of the motion controller in this simulation degrades significantly.
This is due to the fact that the reference trajectory adopted in this study is far more
complex than the pre-calculated reference trajectories as stated in Equations (4.15) to
(4.20). Besides, high value of Kp has an adverse effect on the stability of the robotic
motion controller system resulting in rigorous fluctuation of the track errors. This
might be resolved by increasing the value of Kd at the expense of degrading the
precision of the trajectory tracking control.
73
From Figures 4.5 (d) to (f), the most critical period is observed to occur
within the time range 15 – 20 s. At this stage, the mobile robot experiences the
largest change of heading direction. As a result, this causes the track errors for x to
increase drastically. However, due to nonholonomic constraints, the track errors for y
experiences a slight change only, considering the virtual WMR satisfies the pure
rolling and non-slipping conditions.
Figures 4.5 (g) and (h) illustrate the computed torques for the right and left
motors respectively. With the incorporation of AFC into the motion controller
scheme, the system is able to compute the necessary applied control torque that is
required to cancel out the disturbances. However, the computed torques increase
drastically whenever the virtual WMR is required to change its heading direction as
observed in Figures 4.5 (g) and (h) at a steady state condition. This consequently
leads to the saturation of the computed torques, and thus results in prolonged
convergent time of the motion controller.
The sharp increase of the computed torque is due to the abrupt change of
inertia of the WMR plus the effect of friction whenever the robot is required to turn
suddenly. One way to counter this problem is to ensure a more gradual turning of the
WMR through proper path planning and control. This also involves appropriate
acquisition of WMR and controller parameters particularly the good estimation of the
IN (inertia matrix) parameter in the AFC loop and the controller gains.
74
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 4.5: Performance of the simulator under various loading conditions
75
To promote better understandings of the simulation results involving the
physical workspace of the mobile robot, the technology of VR has been applied.
Figures 4.6 (a) – (h) illustrate several views of the virtual WMR simulator.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 4.6: Several views of the constructed virtual WMR simulator
76
By displaying the simulation results graphically, the interactivity between the
virtual WMR and its VE can be analyzed in greater depth. Therefore, the knowledge
gained through the simulation can then be used for the experimentation of physical
WMR in real world.
4.8 Conclusion
The developed virtual WMR simulator has been proven to be very effective
as the results of the experiments suggest. It is observed that the mobile robot is able
to autonomously plan for a global collision-free path which is then transformed into a
time-indexed trajectory through the proposed trajectory planner algorithm. With this
generated trajectory, the proposed motion controller has successfully driven the
virtual WMR to follow the reference path although it is disturbed by a number of
introduced ‘noises’. The AFC scheme is found to be robust and effective in the
generation of the compensated torques required for the control action. On the whole,
it can be deduced that the main contribution of the developed virtual WMR simulator
is that it has successfully provided a useful platform (through the construction of an
imaginary world) for the testing of robot control algorithms. This has direct
consequence on the possible reduction of the experimentation costs as well as the
fact that it may serve as a training environment (e.g. on safety aspect and layout
planning) for the prospective researchers/users.
CHAPTER 5
RESOLVED ACCELERATION CONTROL AND ACTIVE FORCE
CONTROL (RACAFC) OF MOBILE MANIPULATOR
5.1 Introduction
This chapter discusses the proposed Resolved Acceleration Control and
Active Force Control (RACAFC) scheme for motion control of mobile manipulator
(MM) whose kinematic and dynamic models have been established in Chapter 2. The
robot is a differentially driven wheeled mobile platform with a two-link planar arm
mounted on top of the platform. A simplified coordinate (x, y) and heading angle (φ)
of a nonholonomic mobile manipulator motion control using a class of resolved
acceleration control combined with an active force control strategy is discussed. The
RAC part is used to manipulate the kinematic components while the AFC scheme is
implemented to compensate the dynamic effects including the bounded
known/unknown disturbances and uncertainties. For convenience, the proposed
scheme is called MM-RACAFC (Mobile Manipulator – Resolved Acceleration
Control and Active Force Control), while the scheme without AFC is known as MM-
RAC (Mobile Manipulator – Resolved Acceleration Control).
.
78
5.2 Proposed MM-RACAFC Scheme
The proposed scheme is divided into two categories, i.e., RAC that deals with
the kinematic, and AFC that deals with the dynamics. The RAC implements position,
velocity and acceleration signals with the referenced signals pertaining to the robot
moving in a Cartesian coordinate also defined accordingly. Figure 5.1 shows the
outline of the proposed scheme. From the figure, the proposed RAC is designed to
provide the stability of the system performance and the convergence of the system’s
error. The AFC is proposed to specially compensate the non-linearity of the
dynamics including disturbances. Even in fact the RAC is a converge (negative)
feedback control that able to stabilize the system and converging the general error
occurred but however the high non-linearity would be relatively uncompensated due
to the performances limitation of the position & speed control (only) of the RAC
(Muir and Neumann, 1990, Musa, 1998, Campa, et. al., 2001). Therefore, the
proposed AFC is specially designed to solve this problem.
Figure 5.1: Outline of the proposed MM-RACAFC scheme
The proposed RACAFC controller is made up of two controllers that could be
theoretically designed independently. The complete proposed MM-RACAFC scheme
is shown in Figure 5.2.
Kinematics Problem Dynamics Problem
Using RAC on (xF, yF, φ, xE, yE) control
Using AFC on (θmotorL, θmotorR, θlink-1, θlink-2)
control
RAC-AFC
79
RAC Controller
Inverse Kinematic
AFC Controller
InverseDynamic of
Mobile Manipulator s
1 s1
Direct Kinematic
actθ&& actθ& actθ++
-
Q
+
actualqq ),( &
desiredqq ),( &
+
+
′, actθ ′&&
Figure 5.2: The proposed MM-RACAFC scheme
From Figure 5.2, the AFC is serially configured to the RAC so that basically
the RAC can be tested without the AFC. In this case of without AFC the output of
RAC (after transformed to angles domain of actuators) can be directly connected to
the actuators (motors). For the RAC only the scheme can be redrawn as shown in
Figure 5.3.
RAC Controller
Inverse Kinematic Motors
InverseDynamic of
Mobile Manipulator s
1 s1
Direct Kinematic
actθ&& actθ& actθ++
-
Q
+
actualqq ),( &
desiredqq ),( &
Figure 5.3: The MM-RAC scheme
For comparative study the scheme as shown in Figure 5.3 was also simulated
and the results would be compared to the results on the scheme as depicted in Figure
5.2. Note that the two schemes would be represented in one schematic simulation
diagram (will be discussed later).
80
The RAC part can be described as shown in Figure 5.4.
Kd
Kp
comq&&refq&&
refq&
refq
+
+
-
-
++
++
actq&
actq
RAC
err
Figure 5.4: The RAC controller
From Figure 5.4, for q generalized coordinates of TEEFF yxyxq ],,,,[ ϕ= in
real number nℜ the output equation of the RAC can be written as:
)()( actrefactrefrefcom qqKpqqKdqq −+−+= &&&&&& (5.1)
The AFC controller in Figure 5.2 operates in acceleration mode. Its input is
the transformed RAC output in angles domain of the motors. Figure 5.5 shows the
schematic diagram of the AFC.
IN/Ktn Ktn
1/Ktn
H-1refθ&&
++
Q
Q'
-+
++ actθ&& Im
IN
Inverse Dynamics
of MM
τ ′
transducer transducer
act
Figure 5.5: The proposed AFC controller
81
In Figure 5.5, IN is the mass moment of inertia matrix estimator (multiplier
constant or function), Ktn is the motor constant, Im is the motor current, is the
actuated motor’s torque, act is the actual total applied motor’s torque, ′ is the
measured actuated motor’s torque, Q is the bounded known/unknown disturbances,
and Q′ is the estimated disturbances. ′ can be simply measured using a torque sensor
or by measurement of the actual motor current multiplied with the motor constant.
With reference to Figure 5.5, the simplified dynamic model of the system can
be expressed as:
actact IQ θθττ &&)(=+= (5.2)
where )(θI is the mass moment of inertia of the wheels and arms, and θ is the angle
at each wheel or joint, actθ&& is the angular acceleration of the moving body.
Also from Figure 5.5, a measurement of Q′ (i.e., an estimate of the
disturbances, Q) can be obtained such that:
NIQ act ′′−′=′ θτ && (5.3)
where the superscript ′ denotes a measured or estimated quantity. The torque ′ can
be measured directly using a torque sensor or indirectly by means of a current sensor.
Thus, Equation (5.3) can also be written as:
NIKtnIQ actm ′′−′=′ θ&& (5.4)
where Im’ is the measured motor current.
For the AFC system in Figure 5.5, the actuated motor’s torque can be written
as:
82
KtnKtnQ
KtnNIref
⎟⎟⎠
⎞⎜⎜⎝
⎛ ′+′
=θ
τ&&
(5.5)
Substituting Equation (5.4) into Equations (5.5) and (5.2), we obtain
( )
( ) KtnINI
KtnININI
KtnKtn
NIKtnIKtn
NI
mactref
mactref
actmref
′+′−′=
′+′′−′=
⎟⎟⎠
⎞⎜⎜⎝
⎛ ′′−′+′
=
θθ
θθ
θθτ
&&&&
&&&&
&&&&
(5.6)
and
( ) QKtnINI mactrefact +′+−′= θθτ &&&& (5.7)
Equation (5.6) is known as the AFC controller’s output equation. It has been
ascertained that if the measured or estimated values of the parameters in the equation
were appropriately acquired, a very robust system that totally rejects the disturbances
is achieved (Hewit and Burdess, 1981).
Finally, the proposed MM-RACAFC can be redrawn in one schematic
diagram as shown in Figure 5.6.
IN/Ktn Ktn
1/Ktn
H-1
s1
s1
IN
refθ&&
++
?
Q
Q'
-+
++coordinate
transformation
Kd
Kp
coordinate transformation
coordinate transformation
θθ& actθ&& Imcomq&& refq&&
refq&
refq
+
+
-
-
+ +
+ +
actq&
actq
Inverse Dynamics
of MM
AFC
RAC
?act
transducer
τ ′
transducer
Figure 5.6: Schematic diagram of the proposed MM-RACAFC
83
In Figure 5.6, the subscripts of ref, com and act denote the reference,
command and actual respectively. Considering TEEFF yxyxq ],,,,[ ϕ= generalized
coordinates, output equation of the RAC, TEcomEcomFcomFcomFcomcom yxyxq ],,,,[ &&&&&&&&&&&& ϕ=
consists of five controllers’ output equations, i.e.:
)()( actFrefFactFrefFrefFFcom xxKpxxKdxx −+−+= &&&&&& (5.8)
)()( actFrefFactFrefFrefFFcom yyKpyyKdyy −+−+= &&&&&& (5.9)
)()( actrefactrefrefFcom KpKd ϕϕϕϕϕϕ −+−+= &&&&&& (5.10)
)()( actErefEactErefErefEEcom xxKpxxKdxx −+−+= &&&&&& (5.11)
)()( actErefEactErefErefEEcom yyKpyyKdyy −+−+= &&&&&& (5.12)
where the subscript terms ref, act and com are the input reference, actual output and
command respectively. Kp and Kd are the proportional and derivative gains
respectively.
The AFC part is composed of four output equations in which each equation is
related to each of the motor, i.e.:
( ) 111111 KtnINI mactref ′+′−′= θθτ &&&& (5.13)
( ) 222222 KtnINI mactref ′+′−′= θθτ &&&& (5.14)
( ) LmLLactLrefLL KtnINI ′+′−′= θθτ &&&& (5.15)
( ) RmRRactRrefRR KtnINI ′+′−′= θθτ &&&& (5.16)
where the subscripts 1, 2, L, and R denote motors of the link-1, link-2, left and right
wheels respectively.
84
5.3 Proposed RACAFC for Mobile Platform Section
The successful implementation of AFC to the mobile manipulator partly
depends on the feasibility of AFC applied to the mobile platform which has
nonholonomic constraints. Before discussing the simulation on the proposed MM-
RACAFC, an investigation into the RACAFC scheme applied to the mobile platform
is firstly presented in the following paragraphs.
Differentially Driven Mobile Robot (DDMR) normally employs two
independently driven wheels with a common axis and a castor to add to the stability
of the platform. This mobile platform can be classified as a nonholonomic system
such that the nonholonomic constraint cannot be expressed as time derivatives of
some functions of the generalized coordinates. The use of DDMR as a mobile robotic
system has been considered a challenging research area that is rigorously being
studied by many researchers, either in kinematics or dynamics domain. In the
proposed MM-RACAFC scheme this type of DDMR is used as platform of the
mobile manipulator.
A number of nonholonomic mobile robot tracking control methods has been
proposed: velocity and heading angle (v, ω) control (Kanayama, e. al., 1990),
intelligent steering control and path planning using genetic algorithm (Yasuda and
Takai, 2001) and an improved (v, ω) control with exponential stabilization using
Lyapunov’s stability technique (Pourboghrat, 2002). The models used in the cited
works are more concerned about the kinematics and the studies mostly relate to
establishing the mobile robot’s stability under varied initial conditions and trajectory
input functions. Other researchers focus on the robust motion control such as using
backstepping kinematics to dynamics method (Fierro and Lewis, 1995), (v, ω)
control converted to torque control combined with neural network method (Fierro
and Lewis, 1998) and adaptive control (Fukao, et al., 2000). Their works mainly
centre around the techniques on how to manage the robot dynamics and cancel or
compensate the disturbances. However, they did not address the computational factor
when the methods were to be implemented in real robot programming implying that
the methods are quite complex to be directly written in a compact program.
85
As an initial study, a simplified coordinates (x, y) and heading angle (φ) of
nonholonomic mobile robot motion control using resolved acceleration control
(RAC) combined with active force control (AFC) is discussed. The RAC that was
initiated by Luh, et al. (1980) is a simple but yet powerful acceleration mode control
method that could improve the existing conventional servo control scheme. By
employing the RAC-based x and y control, instead of the v control, the proposed
control scheme would have a more flexible position and speed control. This
flexibility is gained by employing the input references of position, velocity and
acceleration simultaneously. To overcome the dynamics problem related to effect of
disturbances and uncertainties, an active force control scheme, firstly introduced by
Hewit and Burdess (1981), was incorporated into the proposed RAC scheme. The
complete control scheme applied to the DDMR is called as DDMR-RACAFC.
The proposed DDMR-RACAFC consists of two controllers that could be
theoretically designed independently. Firstly, the RAC part consists of three
controllers output equations defined as:
)()( FactFrefFactFrefFrefFe xxKpxxKdxx −+−+= &&&&&& (5.17)
)()( FactFrefFactFrefFrefFe yyKpyyKdyy −+−+= &&&&&& (5.18)
)()( actrefactrefrefe KpKd ϕϕϕϕϕϕ −+−+= &&&&&& (5.19)
where for TFF yxq ],,[ ϕ= and the subscript terms ref, act and e are the input
reference, actual output and error respectively. Kp and Kd are the proportional and
derivative gains respectively. For application of the RAC scheme only, the controller
output parameters with subscript e could be directly connected to the actuators input.
The AFC part was designed to operate in the acceleration mode of each motor at the
angular side of each wheel. The proposed AFC scheme is shown in Figure 5.7.
86
IN / Ktn Ktn
1/Ktn
DDMR+
+
Tq
Q
Q′
-+
++θ ref
IN
θ act .. ..
Figure 5.7: The proposed AFC applied to the DDMR
Q indicates the bounded (known or unknown) disturbances, Ktn is the motor
constants (left and right), IN is the estimated inertia matrix, and Q′ is the estimated
disturbances calculated by the AFC algorithm. IN should be adjusted properly to
trigger the disturbances cancellation process. The simulation of DDMR-RACAFC
was then performed. The advantage of using the RACAFC scheme to perform the
motion control with capabilities of compensating the effects of disturbances shall be
rigorously investigated and presented in subsequent sections.
5.4 Simulation
The simulation consists of three schemes, i.e., RACAFC for mobile platform
(DDMR-RACAFC), MM-RAC, and MM-RACAFC. The first scheme was used to
test the convergences and controllability of the RAC combined to AFC in the case of
nonholonomic constraint in the mobile platform. The results would be then applied to
the proposed MM-RACAFC. The second simulation, i.e., MM-RAC was performed
to test the performance of the RAC scheme without AFC in the case of mobile
manipulator. The third, as the main proposed scheme in this chapter was simulated
and then compared to the results of the MM-RAC scheme. All the schemes are
simulated using MATLAB and Simulink software package.
87
5.4.1 Simulation Parameters
The simulations of MM-RAC and MM-RACAFC use same parameters for
the robot’s physical properties, task, the defined disturbances, the main control
parameters (i.e., Kp, and Kd), and the method of simulation and its parameters.
Tables 5.1, 5.2 and 5.3 show the specifications of the mobile manipulator, the
prescribed trajectory (task) and the disturbances respectively. Data of the control
parameters will be described later related to the simulation results.
Table 5.1: Specifications of mobile manipulator
Parameters Mobile Platform Manipulator
Type Differentially-Driven Mobile Robot (left & right)
Two-link Planar Arm
Mass of platform 40 kg Mass of wheel 1 kg (each) Half width of platform 0.4 m Mass moment of inertia of platform about vertical axis
11.525 kg.m2
Mass moment of inertia of wheel about wheel diameter
0.05 kg.m2
Mass moment of inertia of wheel about wheel axis
0.05 kg.m2
Radius of wheel 0.11 m Distance of point G to F 0.3 m Mass of link-1 (plus motor at joint 2) 3.25 kg Length of link-1 0.4 m Length of link-1 from joint-1 to centre of gravity
0.24 m
Mass moment of inertia of link-1 about joint-1 axis
0.0433 kg.m2
Mass of link-2 (plus gripper) 1.25 kg Length of link-2 0.38 m Length of link-2 from joint-2 to centre of gravity
0.21 m
Mass moment of inertia of link-2 about joint-2 axis
0.0151 kg.m2
Motor constant of joint-1 0.0625 Nm/Ampere Motor constant of joint-2 0.0371 Nm/Ampere Motor constant of left wheel 0.0625 Nm/Ampere Motor constant of right wheel 0.0625 Nm/Ampere Gear ratio of Motor-1 100:1 Gear ratio of Motor-2 200:1 Gear ratio of Motor-L 100:1 Gear ratio of Motor-R 100:1
88
Table 5.2: The prescribed trajectories
Parameters Mobile Platform/Vehicle only
Mobile Manipulator
Type of track See Figure 5.8. See Figure 5.9. Radius of vehicle moving 10 m 10 m Velocity of vehicle 0.4 m/s 0.2 m/s Initial orientation (heading angle)
π/2 radian π/2.4 radian
Radius of “TIP” function 0.14 m Angular speed of arm (TIP) 0.06 m/s Vehicle’s initial position (x, y) (7;0)m (10;0)m Tip’s initial position (x, y) (10.55;0.35)m
Figure 5.8: DDMR Trajectory Figure 5.9: MM Trajectory
Table 5.3: The disturbances
Parameters Mobile Platform/Vehicle only
Mobile Manipulator
Type of disturbances 1. Q-constant 2. Q-pulse 3. Q-vibration
1. Q-constant 2. Q-impacts 3. Q-vibration
Constant torques at wheels L/R (5;-5) Nm RAC only: 0, ±0.1, ±0.2 Nm RACAFC: ±2, ±5, ±20 Nm
Constant torques at link-1 &link-2 RAC only: 0, 0.1, 0.2 Nm RACAFC: 1, 5, 20 Nm
Frequencies of Q-pulse at (L;R) wheels (1;1) Hz Amplitudes of Q-pulse at (L;R) wheels (5;5) Nm Frequencies of Q-sine at (L;R) wheels (5;5) Hz 0.06 m/s Amplitudes of Q-pulse at (L;R) wheels (5;5) Nm (10;0)m Impact Forces See Figure 5.10. Vibration Excitations See Figure 5.11.
89
The impact disturbance was defined as a serially impact signals as shown in
Figure 5.10 considering the robot operation at conditions with an instant collisions at
the tip and holes or bumps at the terrain surface. We also applied vibration at each
joint and wheel as depicted in Figure 5.11.
Figure 5.10: Impact Signals Figure 5.11: Vibration Signals
The frequencies and amplitudes of the impact forces and vibration excitations
are shown in Table 5.4.
Table 5.4: Properties of impact and vibration disturbances
Parameters Impact Vibration
Frequency at link-1 15 Hz 20 Hz Amplitude at link-1 (0.9;-0.45) Nm 0.3 Nm Frequency at link-2 15 Hz 18 Hz Amplitude at link-2 (0.9;-0.45) Nm 0.3 Nm Frequency at wheel-L 15 Hz 14 Hz Amplitude at wheel-L (5;-2.5) Nm 2 Nm Frequency at wheel-R 15 Hz 14 Hz Amplitude at wheel-R (5;-2.5) Nm 2 Nm
The simulation methods and its parameters are shown in Table 5.5.
90
Table 5.5: Simulation methods and parameters
Parameters DDMR Mobile Manipulator
Start Time 0 s 0 s Stop Time 15 s 30 s Solver ODE45 (Dormand-Prince) ODE45 (Dormand-Prince) Stepping method Variable-Step Max. step size 0.1 0.1 Min. step size 0.001 0.001 Initial step size 0.001 0.001 Relative tolerance 0.001 0.001 Absolute tolerance auto auto
5.4.2 Simulink Block Diagrams
The simulation consists of three AFC-based schemes, i.e., DDMR
(Differentially Driven Mobile Robot)-RACAFC, MM-RAC, and MM-RACAFC.
Figures 5.12, 5.13, and 5.14 depict the Simulink diagram of DDMR-RACAFC, MM-
RAC, and MM-RACAFC respectively. For the DDMR-RACAFC, the scheme
without AFC can be selected by clicking the Selector in Figure 5.12.
Figure 5.12: Simulink diagram of DDMR-RACAFC
91
Figure 5.13: Simulink diagram of MM-RAC
Figure 5.14: Simulink diagram of MM-RACAFC
Generally, these three schemes use same Simulink diagrams for certain
functions in the blocks such as the input functions, RAC controller plus inverse
kinematics, direct kinematics, performance display, inverse dynamics, and external
disturbances. Each block in the diagram of DDMR (Figure 5.12) may be considered
as part of the blocks that is related to the MM Simulink diagrams (Figures 5.13 or
5.14). The block of Mobile Platform Input Function in Figure 5.15 is used as the
input of DDMR-RACAFC simulation. Its detailed schematic is shown in Figure
5.16.
92
Figure 5.15: Simulink diagram of the input functions for MM simulation
Figure 5.16: Simulink diagram of the Mobile Platform Input Function
Figure 5.17 shows the diagram of Tip Position Input Function. It is noted that
the desired acceleration, whether for the mobile platform or the tip of arm, should be
set according to span of the respective desired speed and position.
93
Figure 5.17: Simulink diagram of the Tip Position Input Function
Figure 5.18 shows the diagram of RAC Controller plus Inverse Kinematics
section. The inverse kinematics is composed of inverse kinematics for the
manipulator and for the platform. Figures 5.19 and 5.20 depict the Simulink
diagrams of the respective blocks.
Figure 5.18: Simulink diagram of the RAC Controller plus Inverse Kinematics section
94
Figure 5.19: Simulink diagram of Inverse Kinematics of the manipulator
Figure 5.20: Simulink diagram of Inverse Kinematics of mobile platform
The diagram shown in Figure 5.20 is the inverse kinematics of mobile
platform or DDMR. This block can be particularly used as the inverse kinematics
section for DDMR simulation as in Figure 5.12. It is highlighted that transformation
matrix S*(q) is as highlighted in Chapter 2.
The direct kinematics of the platform and the manipulator arm can be simply
combined in one diagram as shown in Figure 5.21. Figures 5.22 and 5.23 depict the
particular kinematics diagram for the respective platform and manipulator.
95
Figure 5.21: Simulink diagram of Direct Kinematics of MM
Figure 5.22: Simulink diagram of Direct Kinematics of manipulator
Figure 5.23: Simulink diagram of Direct Kinematics of mobile platform
96
For convenience, to analyze the simulation results in real-time, we applied an
‘animation’ procedure. Some of the important data of the robot operation such as the
actual position of the platform (subject to point F) and of the tip (subject to point E)
were also recorded in Performance Display section. Its diagram is shown in Figure
5.24.
Figure 5.24: Simulink diagram of Performance Display section
Figure 5.25: Simulink diagram of Inverse Dynamics of MM
97
The dynamics of the mobile manipulator consists of two parts, i.e., the
DDMR and manipulator. In this study, we have neglected the interaction torques
among the platform and the manipulator by considering the robot moving at
relatively low speed, taking into account that the control problems of the platform
and that of manipulator arm have been well understood (Kolmanovsky and
McClamroch, 1995). Figure 5.25 shows a Simulink block diagram representing
dynamics of mobile manipulator as mentioned earlier. Figures 5.26 and 5.27 are the
dynamic constraint matrix, M(q) and overall dynamics of the manipulator (arm)
respectively.
Figure 5.26: Simulink diagram of the constraint matrix M(q)
Figure 5.27: Simulink diagram of the manipulator’s dynamics
98
5.5 Results and Discussion
The discussion of the simulation results obtained is divided into in two topics,
i.e., based on DDMR simulation and MM simulation. For both simulations, RAC and
or RACAFC schemes have been implemented. The analysis is concerned on the
performances comparison between the two control concepts.
5.5.1 RACAFC for DDMR
The initial experiment is to determine appropriate Kp and Kd values of the
RAC section (see Figure 5.12). The tuning process was performed in the RAC mode
using a trial-and-error method. Some disturbances were also considered during the
tuning process. By using the tuned Kp and Kd values, a number of experiments were
performed to include the AFC scheme. The IN value was then tuned. It was obtained
through a heuristic method. The range of the IN from 1 to 2.8 kgm2 was optimized
manually with a step of 0.1 kgm2. The consideration was based on the minimum
average of the tracking error’s root mean square.
From the initial investigation on the RAC, the optimum Kp and Kd for T
FF yxq ],,[ ϕ= were obtained as follows:
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
005.0000350000350
Kp ⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
0015.0000320000320
Kd (5.20)
It should be noted that the Kp and Kd (0.005 and 0.0015 respectively) for the
robot’s heading angle control are relatively very small compared to those of the
robot’s movement control. This is due to the fact that the heading angle control is
very sensitive in the proposed (x, y, φ) kinematics control mode. These control
parameter values would be applied to the next investigation employing the AFC
99
scheme, initially to tune the IN value. Figure 5.28 shows the result of the IN tuning
process.
Figure 5.28: Results of IN tuning (the white bar indicates the optimum value)
From Figure 5.28, it can be deduced that the optimum IN is around 2.4 kgm2.
This value was then used as the reference IN for testing the robustness of the
proposed DDMR-RACAFC scheme. IN can be written as:
⎥⎦
⎤⎢⎣
⎡=
4.2004.2
IN (5.21)
Figure 5.29 shows the Trajectory Tracking Error (TTE) of the two schemes
with and without disturbances. The disturbances were defined as a horizontal
sinusoidal force applied to each wheel with amplitude of 5 N and frequency of 5 Hz
as described in Table 5.3.
Figure 5.29 (a): TTE with no disturbances Figure 5.29 (b): TTE with disturbances
100
From Figure 5.29, it is obvious that the RACAFC method demonstrates its
potential, particularly when the sinusoidal type disturbance is applied. The
disturbance is significantly compensated and the errors generated were far less than
shown by its counterpart. The average steady state error for the RAC method is
around 20 mm in average but the RACAFC scheme successfully suppresses the error
to less than 1 mm. The superiority of the AFC is easily concluded from the graphic
‘animation’ as shown in Figure 5.30.
Figure 5.30 (a): Robot Animation for the RAC
Figure 5.30 (b): Robot Animation for the RACAFC
For the robot overall dimension of 80×80 cm and the input task of curve
tracking with a radius of 10 m, the track errors generated for both schemes, i.e., 2 cm
and 0.1 cm are relatively not significant considering a regular mobile robot tracking.
For a very high precision robot task planning and trajectory tracking, then the results
based on accuracy are truly significant and meaningful. The result however
highlights the great potential of the RACAFC scheme for this kind of application.
5.5.2 Mobile Manipulator Control
By considering the simulation results on DDMR system mentioned earlier
and the results of the RACAFC applied to robot arm reported in Musa (1998) and
Pitowarno (2002) the proposed MM-RACAFC could be conveniently performed.
101
Equations (5.8) to (5.12) and (5.13) to (5.17) can then be combined into an integrated
motion control as well. As it is, there are five parts of RAC and corresponding five
parts of AFC that were created and that the overall control scheme should be run
simultaneously. The optimum IN of the mobile platform that has been obtained from
previous investigation, i.e., [ ]2.4 4.2diag=IN was used for the mobile platform of the
MM.
5.5.2.1 Simulation Procedure
The optimum Kp, Kd and IN that have been acquired in the RACAFC applied
to DDMR were again used as the initial crude values to investigate the arm of the
MM. The complete simulation procedure is depicted in Figure 5.31.
Figure 5.31: A flow chart showing the simulation procedure
Start
Prepare: MM-RAC only scheme. Set Kp & Kd of platform to as in
Equation 5.20
Set Kp & Kd of Arm using heuristic method.
Set disturbance to be disable.
Simulate
Are errors OK?
Tune Kp & Kd of Arm
Retune Kp & Kd of platform & arm with (relative) small values adjusment.
Introduce some disturbances.
Prepare: MM-RACAFC scheme. Set all Kp & Kd and IN based on the previous results except IN of arm.
Set IN of arm to any small value (heuristic). For initial inestigation, set the platform not moving.
Simulate
Tune INof Arm
Are errors OK?
Introduce disturbances
Perform simulations using the optimum parameters obtained. Test at several
types of disturbance defined.
Record all data obtained. Analyse the results.
END
Retune Kp & Kd of platform & arm with (relative) small values
adjusment. Set platform to move.
Yes
No
No
Yes
102
The initial experiment was to determine the appropriate values of Kp and Kd
of the RAC section. The tuning process was performed in the RAC mode using a
heuristic method considering some disturbances in the process. By using the tuned
Kp and Kd values, a number of experiments was then performed to include the AFC
scheme. The IN value was also approximated in the same manner. For the mobile
platform, the range of the IN value from 1 to 2.8 kgm2 was optimized manually with
a step of 0.1 kgm2 as depicted in Figure 5.7. It was based on the minimum average of
the tracking error’s root mean square. For the arm or manipulator, its IN value was
tuned by considering the platform not moving.
From Figure 5.31, it should be noted that the procedural step of retuning all
the control parameters after the errors validation (at the left & right parts) using a
very small values adjustment (up and down) was needed to refine the errors. In a
heuristic or trial-and-error method this approach usually can improve the results
although not always significant (Franklin, et al., 2002).
To clearly illustrate the potentials of the AFC that is incorporated into the
RAC scheme, an analysis and discussion will be presented through a comparison
study of the graphical results obtained. The discussion shall deal with the following
headings:
• The optimum Kp, Kd and IN obtained.
• Effects of the constant torque disturbance.
• Effects of the impact disturbance.
• Effects of the vibration disturbance.
5.5.2.2 The Optimum Kp, Kd and IN obtained
The first procedure was to tune the Kp and Kd of the RAC using a heuristic
method. Note that, in fact, the optimum Kp and Kd of the RAC was different with the
103
Kp and Kd of the RACAFC. Kp and Kd are expressed in diagonal matrices in the
form:
ϕKpKpKpKpKpdiagKp yFxFxExE= (5.22)
and Kd is:
ϕKdKdKdKdKddiagKd yFxFxExE= (5.23)
The results are shown in Equations (5.24) and (5.25). The RAC would be
then evaluated using its optimum Kp and Kd as follows:
004.04504505.1315diagKpRAC = (5.24)
0017.03203201213diagKd RAC = (5.25)
Next, the optimum Kp, Kd, and IN of the RACAFC was investigated using
the same method. The results are shown in Equations (5.26), (5.27) and (5.28) as
follows:
004.0450450350350diagKpRACAFC = (5.26)
0017.0320320320320diagKd RACAFC = (5.27)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
4.200004.200000675.000000675.0
000000000000
2
1
R
L
ININ
ININ
IN
(5.28)
It is noted that the values shown in Equations (5.26) and (5.27) are the refine-
tuned Kp and Kd of the integrated kinematic control of the MM. The IN was then
considered as the basic (crude) value for further experimentation.
104
5.5.2.3 Effects of Constant Torque Disturbance
Several types of constant torque (Qc) disturbances were introduced to the
schemes. Qc is defined as:
[ ]TRL QcQcQcQcQc 21= (5.29)
where Qc1 is constant torque disturbance at joint-1, Qc2 at joint-2, QcL at wheel-L,
and QcR at wheel-R, and for the introduced disturbances we have used three types of
Qc for the MM-RAC, and the other three types for MM-RACAFC, i.e.:
a. [ ]TQc 0000= Nm (as no disturbances) for MM-RAC,
b. [ ]TQc 05.005.001.001.0 −= Nm for MM-RAC,
c. [ ]TQc 1.01.002.002.0 −= Nm for MM-RAC,
d. [ ]TQc 5.05.02.02.0 −= Nm (as small Qc) for MM-RACAFC,
e. [ ]TQc 5522 −= Nm (as high Qc) for MM-RACAFC, and
f. [ ]TQc 20202020 −= Nm (as very high Qc) for MM-RACAFC.
The different Qc’s were applied to the two by considering the RACAFC was
known very robust compared to the RAC only. Figure 5.32 depicts the error (TTE) at
the tip end position for the MM-RAC and MM-RACAFC schemes.
Figure 5.32 (a): TTE of Arm for MM-RAC at Qc
Figure 5.32 (b): TTE of Arm for MM-RACAFC at Qc
105
Figure 5.32 (a) clearly shows that the RAC has no ability to adapt if the
operation condition is changed with the introduced disturbances. The increases of
constant torques disturbance obviously degraded the RAC performance. At only Qc
= [0.02;0.02;0.1;-0.1] Nm which relatively can be considered as the operation
without disturbance (very small) the error has increased more than 1 mm peak-to-
peak (indicated by the red line). In contrast, the RACAFC shows the robustness as
depicted in Figure 5.32 (b). The applied disturbances at 0.5 to 20 Nm at the joints
have been rejected by the AFC as well, and all the errors were compensated to less
than 0.15 mm. Although the AFC is basically non adaptive scheme, but at this
juncture, the term of active in active force control can be meant that the control is
directly adaptable to the changes of the operation condition.
Figure 5.33 shows the generated errors of the two schemes at the body
(subject to point F in Figure 2.1(b) of Chapter 2).
Figure 5.33 (a): TTE of Body for MM-RAC at Qc
Figure 5.33 (b): TTE of Body for MM-RACAFC at Qc
The RACAFC also shows the robustness in the case of motion control with
constant torques disturbance on the mobile platform as shown in Figure 5.33 (b). On
the contrary, the performance of the RAC was gradually degraded when the
disturbances was increased as shown in Figure 5.33 (a). At only a relative small
disturbance, i.e., Qc = [0.02;0.02;0.1;-0.1] Nm at the joints and wheels, the error
becomes three times bigger (indicated by the red line) than at the condition without
disturbance (indicated by the blue line).
106
5.5.2.4 Effects of Impact Disturbance
Next, the proposed MM-RACAFC has been evaluated by introducing the
impacts as depicted in Figure 5.10. We have used the term of Qgain as a disturbance’s
gain factor that
maxQimpQQimp gain ×= (5.30)
where Qimp is the applied impacts, and Qimpmax is the maximum impacts
disturbance (Qgain = 1). Qgain is also used in the term of vibration (discussed later).
The impact disturbance (and the other defined disturbances) in the simulation
model can be activated by selecting the parameters in a window of dialog box (by
clicking the icon of the related block at the simulation diagram) as shown in Figure
5.34.
Figure 5.34: The dialog box for External Disturbance Section
The disturbance status (Qstatus) in the window can be set to a value, 0 for
disable, 1 for (full) enable, and 0< Qstatus <1 to indicate the disturbance attenuation
(or Q in the case of impacts). The impacts have been applied to the two schemes in
107
three conditions, i.e., small (Qgain = 0.1), regular (Qgain = 0.5), and high impact (Qgain
= 1). Figure 5.35 shows the response of MM-RAC and MM-RACAFC at the arm
subjects to point E in Figure 2.1 (b) which the impacts is initially introduced at time
of t = 8.5 s for the joints, and t = 10 s for the wheels. As can be seen, the RACAFC
responds to the impacts disturbance much better that the RAC only does. The RAC,
as aforementioned in the case of constant torques disturbance, could not adapt the
change of condition of operation. Increasing Qgain = 0.1 to Qgain = 0.5 affects the
error to increase to more than twice (less than 2 mm to 4 mm) as depicted in Figure
5.35 (a). On the contrary, the RACAFC remains stable and succeed to reject the
impacts to less than 0.3 mm of the error at maximum impacts (Qgain = 1).
It should be noted that the initial error of the RACAFC at t = 0 to 6 is the
error occurred at the initial positioning of the tip regarding to the pose of the arm
when the robot moving just started.
Figure 5.35 (a): TTE of Arm for MM-RAC at Qimp
Figure 5.35 (b): TTE of Arm for MM-RACAFC at Qimp
A robust performance of the RACAFC is also shown in Figure 5.36 (b) in the
case of the impacts occurred at the wheels of the body. The impacts with peak 5 Nm
(See Figure 5.10) imposed to each the wheel has been rejected to less than 0.03 mm.
In contrast, The RAC clearly shows the incapability on compensating the impacts
disturbance as depicted in Figure 5.36 (a). The error is around ten times higher than
the error on the RACAFC scheme.
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Figure 5.36 (a): TTE of Body for RAC at Qimp
Figure 5.36 (b): TTE of Body for RACAFC at Qimp
It is noted that the errors of the arm in Figures 5.35 (a) and 5.35 (b) are the
accumulated errors of the body and the arm itself because of the arm is mounted on
the top of the body. As can be seen, when the body’s error is increased at t = 11 s, as
shown in Figure 5.36 (a), the error of the arm is also increased. Particularly, in the
case of RAC only it can be deducted that RAC has no capability to regulate
disturbance effects of the interaction among the body to the arm.
5.5.2.5 Effects of Vibration
Vibration typically occurs in real world robotic application. In a mobile
system it maybe occurred at wheels on small waving surface of road or terrain where
the robot moves. The vibration on wheels can serially affect to the joints of arm,
moreover at the tip end position. In the simulation, vibrations at relative low
frequencies were defined. With reference to Figure 5.11, the vibrations, Qvib, were
defined to be 14 Hz at wheel-L and wheel –R with amplitude of 2 Nm, and 20 Hz at
joint-1 and 18 Hz at joint-2 with amplitude of 0.3 Nm respectively. The vibrations
were introduced to the robot operation during the trajectory tracking. Figure 5.37
shows the effects of the vibration for the MM. Again, the proposed RACAFC
exposes the superiority in compensating the high non-linear disturbance such as the
defined vibrations. The error of arm of the RACAFC is only less than 0.2 mm at the
largest vibration (Qgain = 1) while of the RAC is more than 3 mm. Although the
applied AFC only used a basic (crude) approximation on estimating the inertia
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matrix of the mass moment of the MM, the advantage of the proposed RACAFC is
clear and meaningful. In addition, RAC and AFC can be simply considered as a
general robust motion control of the mobile manipulator.
Figure 5.37 (a): TTE of Arm for MM-RAC at Qvib
Figure 5.37 (b): TTE of Arm for MM-RACAFC at Qvib
Figure 5.38 (a): TTE of Body for MM-RAC at Qvib
Figure 5.38 (b): TTE of Body for MM-RACAFC at Qvib
Figure 5.38 also shows the error refinement at the body subjects to point G.
Though at the initial tracking (t = 0 to 5 s) the error is relatively high (because of the
process to reach steady state), but however, the vibration was cancelled by the
RACAFC to less than 0.03 mm, while the RAC has suppressed the vibration at 0.08
mm only.
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5.6 Conclusion
Three major conclusions can be drawn from the study carried out in this
chapter:
.
• The advantage of using the RACAFC scheme to perform the motion control of
the DDMR with capabilities of compensating the effects of disturbances is
demonstrated. The technique was found to be superior to using RAC only. The
RAC only scheme is found to be feasibly applied to nonholonomic motion
control of the system, thereby providing another alternative means of controlling
the system other than the existing (v, ω) control. The RAC scheme augmented
by combining the RAC with AFC strategy to the motion control of the system is
considered as a totally new approach. However, a number of experimentation
needs to be carried out to further explore the potential of the scheme when other
different tasks, parameters or operating and loading conditions are considered.
• The proposed MM-RACAFC was successfully proven as a stable and robust
motion control for mobile manipulator in this study. By using only the
‘proportional’ AFC thru optimizing the fixed IN the proposed scheme was
capable to improve the RAC as a robust MM motion control.
• The proposed method successfully exhibits the system’s robustness even in the
presence of the introduced disturbances in the form of constant torque
disturbance, impact and vibration forces.
CHAPTER 6
RESOLVED ACCELERATION CONTROL AND
KNOWLEDGE-BASED FUZZY ACTIVE FORCE CONTROL
(RACKBFAFC) OF MOBILE MANIPULATOR
6.1 Introduction
In this chapter, a simplified coordinate (x, y) and heading angle (φ) of a
nonholonomic mobile manipulator motion control using RAC combined with a
knowledge based fuzzy active force control (KBFAFC) strategy is presented. The
scheme consists of two main parts that each has particular goal, that are the RAC
deals with the kinematics, and the KBFAFC is designed to tackle the dynamics
problem specifically. By using this RAC-based x and y control the proposed control
scheme would have a more flexible position, velocity and acceleration control. This
flexibility is gained by the use of simultaneous input reference position, velocity and
acceleration parameters. An AFC scheme combined with the proposed knowledge-
based fuzzy system is incorporated into the RAC scheme to tackle the robot’s
dynamic problem particularly those involving disturbances and uncertainties. The
stability and robustness of the proposed RACKBFAFC are investigated through a
simulation study. Several types of disturbances such as static torques, impacts and
vibration are introduced to evaluate the performances. A deliberate analysis would
then be discussed. In the last subsection, the investigation has showed the significant
improvement of the robustness of the proposed RACKBFAFC compared to the
existing RACAFC.
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6.2 Proposed MM-RACKBFAFC Scheme
The proposed scheme as shown in Figure 6.1 is made up of two controllers,
namely, RAC and KBFAFC that can be theoretically designed independently.
s1
s1 refθ&&
coordinate transformation
Kd
Kp
coordinate transformation
coordinate transformation
actθactθ& comq&& refq&&
refq&
refq
+
+
-
-
+
+
+
+
actq&
actq
RAC
actθ&& IN/Ktn Ktn
Mobile Manipulator
1/Ktn
INKBF
+
++
−Q*
Q
++
τ
KBFAFC
τact
×
IN
KBF
AFC Section
Figure 6.1: The proposed MM-RACKBFAFC
In Figure 6.1, the subscripts of ref, com and act denote the reference,
command and actual respectively. Q indicates the bounded (known or unknown)
disturbances, Ktn are the torque constants for the actuating motors (left and right
wheels of the platform and joint-1 and joint-2 of the manipulator), INKBF is the
estimated inertia matrix from the KBF system, and Q* is the estimated disturbance
calculated by the KBFAFC algorithm. The IN′ on the left side is the estimated IN
that is based on the optimum IN obtained from the RACAFC scheme. It is noted that
the input of the INKBF function is the velocities at the joints and wheels.
6.2.1 RAC Section
The RAC applied to the RACKBFAFC is exactly the same as in the previous
RACAFC scheme which has been discussed and established in Chapter 5. RAC is
specifically designed to handle the entire kinematic problem of the MM while the
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scheme of KBFAFC that is incorporated serially to the RAC deals with the dynamic
aspect.
For convenience, the important RAC output equations are rewritten in this
section as follows:
)()( actFrefFactFrefFrefFFcom xxKpxxKdxx −+−+= &&&&&& (6.1)
)()( actFrefFactFrefFrefFFcom yyKpyyKdyy −+−+= &&&&&& (6.2)
)()( actrefactrefrefFcom KpKd ϕϕϕϕϕϕ −+−+= &&&&&& (6.3)
)()( actErefEactErefErefEEcom xxKpxxKdxx −+−+= &&&&&& (6.4)
)()( actErefEactErefErefEEcom yyKpyyKdyy −+−+= &&&&&& (6.5)
The subscripts ref, com, act and e refer to the input reference, command,
actual output and error respectively. Kp and Kd are the proportional and derivative
gains respectively. All controller output equations in Equations (6.1) to (6.5) have
negative feedback elements that contribute to the generation of relevant error signals
that are subsequently coupled with the respective controller gains. In the global MM
motion control, the controller equations can be considered as separated controls but
to be executed simultaneously in real-time.
6.2.2 KBFAFC Section
The KBFAFC is principally an AFC-based scheme in which the IN is
intelligently computed via a knowledge-based fuzzy (KBF) method. Recalling the
output equation of the AFC algorithm in Equations (5.6) and (5.7) and referring to
Figure 6.1, we have:
( ) KtnINI mactref ′+′−′= θθτ &&&& (6.6)
or alternatively, it can be rewritten as:
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KtnININI mactref ′+′′−′= θθτ &&&& (6.7)
In Figure 6.1, the adaptation through the KBF algorithm is imposed on the
INKBF. Thus, the KBFAFC output equation can be written as:
KtnIININ mactKBFrefF ′+′−= θθτ &&&& (6.8)
and the simplified dynamic equation of the system is given by:
QKtnIININ mactKBFrefFact +′+′−= θθτ &&&& (6.9)
with
)( actKBFKBF fIN θ&= (6.10)
where INF is the fixed IN that was obtained as the optimum IN of the existing
RACAFC (established in Chapter 5), and INKBF is the variable or adaptive IN that
should be computed by the KBF algorithm (fKBF) based on the actual velocity actθ& .
The superscript ′ denotes an estimated or measured quantity. The angular velocity to
be controlled (for each joint and wheel) is employed as the respective input function
of fKBF. For KBF design, the knowledge-based reasoning as the basis for the
development of the fuzzy inference mechanism should take into consideration the
knowledge investigation and representation, and knowledge acquisition and
processing. These will be duly presented and discussed in the following subsections.
6.2.3 Knowledge Investigation and Representation
The first procedure to implement the knowledge based fuzzy system is
knowledge investigation. The main aim of this procedure is to ensure sufficient and
appropriate knowledge are gathered for the purpose of reasoning in the process of the
building the fuzzy system that will be applied to the AFC. In a standard knowledge-
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based system, the knowledge can be anything (information/data) that is captured
from the system. In a global view point, the knowledge on mobile manipulator
system and its environments include task specifications, control system
characteristics and its responses and the global constraints (kinematics and
dynamics) of the robot world as can be illustrated in Figure 6.2.
Physical
MM
MM’s Task
MM’s Control
MM’s Environment
Global Constraints
Global Responses
Note: is relation
Figure 6.2: An illustration of global knowledge of mobile manipulator
In principle, we can start investigating knowledge from any node in Figure
6.2. The arrows are used to relate the knowledge being captured to a more concern
view of knowledge in the next relation. In this study we have designed an
investigation procedure that has the direction of ‘flow’ as depicted in Figure 6.3.
Physical
MM
MM’s Task
MM’s Control
MM’s Environment
Global Constraints
Global Responses
1
2
Figure 6.3: The selected semantic networks of the MM’s knowledge structure
Figure 6.3 basically consists of two standard semantic networks. The first
network follows a flow that serially configured as steps of relation of Physical MM
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→ MM’s Task → MM’s Environment → MM’s Control → Global Responses. The
second flow is Physical MM → Global Constraints → MM’s Control → Global
Responses. At this juncture, the two procedural knowledge investigations are
performed with the same most concerned views that are global responses. The node
MM’s Control is used as an overlapping view point that can be more qualitatively
investigated. Following similar methods as those executed by Kuwata and Yatsu
(1997) and Hildebrand and Fathi (2004), the view point of the node MM’s Control
can be expressed as:
,, _' STEPRNcVi ControlsMM∨∪= (6.11)
where Vi is the view point, Nc is the current node, R∨∪ is a set of labels and
STEP is a qualitative investigation. In this study, we have selected a qualitative
investigation that includes the entire previous AFC-based control schemes, the
robot’s tasks and the effects of disturbances (with or without disturbances). Figure
6.4 shows the qualitative investigation in a semantic network that has been adopted
in the study.
Robot Structure
Holonomic constraint
Nonholonomic constraint
Manipulator Mobile Platform
At specific speed
Robot Environment
At specific disturbances
No disturbances
Responses
Control Control Control Control
Robot Task
Figure 6.4: The qualitative investigation in a semantic network
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The nodes of responses in Figure 6.4 are used as qualitative measurements in
which each of the prior node can be inferred to them. Some specified input functions
are then implemented in both simulation and the experimental works so that the
mobile manipulator can be programmed to perform specific trajectory tracking task.
The common control scheme used for both studies is the RACAFC using fixed
inertia matrix estimator. Note that the scheme is applied to both studies prior to the
development of the proposed RAC-KBFAFC scheme. Once the knowledge is fully
acquired from the knowledge investigation procedure, it is then implemented into the
design of the proposed scheme. Illustrations of Features or Knowledge Extraction
Procedure in Knowledge Investigation are shown in Figures 6.5 (a) to 6.5(c). The
figures illustrate how the knowledge required by the proposed system is investigated.
Figure 6.5 (a): The trajectory tracking of the mobile manipulator
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1 cycle 1 cycle 1 cycle 1 cycle 1 cycle
repeating sequences
Simulation: RACAFC
Experiment: RACAFC scheme
1 cycle 1 cycle 1 cycle
error at body
error at arm
(mm
)
1 cycle
repeating sequences
Figure 6.5 (b): The track error at the tip end position for five cycles of repeating
tasks in the simulation
Figure 6.5 (c): The track error at the tip end position for four cycles of repeating
tasks in the experiment
Figure 6.5 (a) depicts the movement of the mobile manipulator in which it
can be seen that the manipulator’s tip position produces a curvy path in the direction
of the robot’s forward movement. Figure 6.5 (b) shows the error signal produced
from the simulation work while Figure 6.5 (c) exhibits the corresponding error curve
based from the experimental study. It is obvious that the error patterns for both
studies are repetitive in nature. Also, it is found that the same input function that is
used in the simulation study which when implemented to the experimental robot,
yields similar error pattern over a period of time. Thus, some features of the track
error signal patterns have been investigated and identified. This information provides
the required ‘knowledge’ for the subsequent implementation of the overall control
scheme. It is evident that the error changes (increases or decreases) continuously
according to specific positions of the robot system during the tracking operation.
Based on the knowledge investigation procedure, some hypotheses can be
deduced as follows:
• There exists a correlation between the track error pattern and the non linearity of
the system dynamics specifically related to the robot motion. In this context, the
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inertia matrix IN of the manipulator can be considered as the non-linear element
of interest.
• The ripples, spikes, and other features of the error pattern show the ‘intensity’ of
the non linearity of the system that occur at specific locations and times.
• Some repeating error signal patterns produced at certain robot motion event could
specifically imply the ‘knowledge’ that could provide a means to improve the
control method. Hence, it is thought to be a wise move such that the effective
robot control action should not take into account the robot motion moving along
the full trajectory but consider only at locations where ‘positive’ definite error
patterns occurred.
Figure 6.6 (a): Angular velocity versus
track error at joint-1 Figure 6.6 (b): Angular velocity versus
track error at joint-2
Figure 6.6 (c): Angular velocity versus
track error at wheel-L Figure 6.6 (d): Angular velocity versus track error at wheel-R at a view ponit
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The response visualized in the respective error signal pattern of the certain
robot operation at the certain condition is then analyzed as shown in Figures 6.6 (a)
to 6.6 (d). In the figures, the notation K denotes the knowledge that is intensively
investigated at particular time instants. From Figures 6.6 (a) and 6.6 (b), it can be
seen that the instant error signal patterns at times denoted by K are unique and
exhibits relationships with the concurrent actual velocity at the joints. It is also
occurred at the wheels as can be seen in Figures 6.6 (c) and 6.6 (d). When the
velocity is changed subjects to the impact disturbance, the error signal pattern on
body is specific. Based on this we then concluded that each of the response can
inherently exhibits the ‘behavior’ of the control, or in short we call the behavior as
the captured knowledge. Table 6.1 shows the representation of knowledge that had
been captured from the investigation.
Table 6.1: The knowledge representation
Prior knowledge
Related knowledge
Relation descriptions Specific Responses
Empirical hypothesis/ suggestion
Robot’s subsystems (joints & wheels)
Partial control (holonomic or nonholonomic)
Each subsystem is controlled partially
Error in each subsystem is unique
Error in each subsystem can be refined partially
Inertia of each subsystem
Uncertainties (of the environment & task)
The uncertainties affect each subsystem specifically
Error in each subsystem is unique
Each of the estimated inertia can be refined specifically
Robot’s specific task
Actual (angular) velocity of each subsystem
Specific task implies specific actual velocity of each subsystem
Case 1: When actual velocity is going to smaller at top curvy velocity, the error is going to larger. Case2: When actual velocity is going to larger at bottom curvy velocity, the error is going to smaller. Case 3: When actual velocity is going to smaller, the error is found large. Case 4: When actual velocity is going to larger, the error is also found small.
- The increased error exhibits that the actual inertia of subsystem is increased or decreased.
- It is therefore the estimated inertia value should be increased or decreased that follows “behavior” of the actual velocity.
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From Table 6.1, the inertia matrix estimation or adaptation can be deduced
that the increased error can be inferred as the condition that the actual estimated
inertia matrix applied to the AFC is going to mismatch. Thus, the applied estimated
inertia matrix should adaptively be increased or decreased regarding the amount of
error. The decision to increase or decrease the applied estimated inertia matrix
depends on the vector (or direction) of the actual velocity.
6.2.4 Knowledge Acquisition and Processing
From the hypotheses deduced, an inference mechanism can be derived. In this
study, the angular velocity of the robot arm is chosen as the indicator (input function)
to describe the relationship between the produced error and the actual velocity. The
output variable to be computed is the estimated inertia matrix, IN of the system that
is necessary for AFC mechanism. Table 1 shows the derived inference mechanism.
Table 6.2: The inference mechanism
Case Part of velocity signal pattern
Related part of error signal
pattern Actions to be taken
1
set IN pattern as top-bottom-top direction
2
set IN pattern as top-bottom-top direction
3
set IN pattern as bottom-top-bottom direction
4
set IN pattern as bottom-top-bottom direction
Note: The basic IN (top value) uses the crude’s
IN = diag0.0675 0.0675 2.4 2.4kgm2
The inference mechanism given in Table 6.2 can be illustrated visually by
studying the graphics shown in Figures 6.7 (a) to 6.7 (d) after the knowledge has
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been taken into account and the output variable has been constructed based on the
input function. The figures illustrate the relationship of velocity and inertia matrix
that subject the joints and wheels.
Figures 6.7 (a) and 6.7 (b) are with the inferred input-output relation of
knowledge at the joints, while Figures 6.7 (c) and 6.7 (d) are for the wheels. In
Figures 6.7 (b) and 6.7 (d), the red dot-line indicate the fixed IN without adaptation
(established in the RACAFC scheme). By incorporating the appropriate relationship
between the input and the output variables, the design of the fuzzy system is clear.
Hence, a simple fuzzy structure is selected to demonstrate the proposed method that
can in turn lead to simple adjustment of the fuzzy specification.
Figure 6.7 (a): Inference input signal of KBF for manipulator
Figure 6.7 (b): Expected output signal of KBF for manipulator
Figure 6.7 (c): Inference input signal of KBF for mobile platform
Figure 6.7 (d): Expected output signal of KBF for mobile platform
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6.2.5 KBF Design
From the procedure of the above knowledge-based method and considering
Tables 6.1 and 6.2 a set of KBF function can be derived as follows:
)( 111 actKBFKBF fIN θ&= (6.12)
)( 222 actKBFKBF fIN θ&= (6.13)
)( actLKBFLKBFL fIN θ&= (6.14)
)( actRKBFRKBFR fIN θ&= (6.15)
where )( 11 actKBFf θ& , )( 22 actKBFf θ& , )( actLKBFLf θ& , and )( actRKBFRf θ& are specific for the
respective joints or wheels. In this study we have considered to design the KBF for
each of subsystem partially in simply form of fuzzy system with single input and
single output rather than designing a universal KBF with four inputs ( 1actθ& , 2actθ& ,
actLθ& , and actRθ& ) and four outputs (INKBF1, INKBF2, INKBFL, and INKBFR). The advantage
of the consideration is the designed partial fuzzy system can be simple and easy to
maintain.
Considering the obvious goal of the fuzzy system design as mentioned above
the proposed RACKBFAFC scheme is then designed as simple as possible. Hence, a
Mamdani type fuzzy with three triangular shaped membership functions (MFs)
representing the input and three Gaussian shaped membership functions of the output
are selected for each input-output relationship. The MFs of the inputs are namely
smaller, normal and larger. We used the term smaller instead of SMALL to
emphasize that smaller is a derived knowledge that more meaningful rather than
SMALL which is merely an information. The MF is typically constructed to
represent the middle (or average) of the input value. Also, the term of larger can be
more meaningful than LARGE with respect to knowledge-based system. It is to
distinguish the meaning of information and knowledge more precisely (Marakas,
1999).
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For the manipulator, normal is set to zero velocity by considering that the
joints move in two directions (clock wise and counter-clock wise) with limited angle
(not more than 180˚ to left or right), and in the operation, zero is the condition in
which the link or joint is not actually moved. For the platform, normal is selected to
be 1.815 rad/s to meet with desired linear velocity of the MM subjects to point F.
However, the setting of normal is adjusted manually with a relative small value by
considering the respective desired angular velocity of joints or wheels. Figures 6.8
(a) to (d) show the implementation of the inference mechanism in the KBF design.
Figure 6.8 (a): MFs of input of joint-1 and joint-2
Figure 6.8 (b): MFs of output of joint-1 and joint-2
Figure 6.8 (c): MFs of input of wheel-L
and wheel-R Figure 6.8 (d): MFs of output of wheel-L
and wheel-R
By considering Figures 6.8 (a) to 6.8 (d) and regarding to Figures 6.7 (a) to
6.7 (d), all the respective KBF system design can be simply done using basic
Mamdani types of fuzzy logic with some considerations as follows:
• AND method: minimum,
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• OR method: maximum,
• Implication method: minimum,
• Aggregation method: maximum, and
• Defuzzyfication method: centroid.
The rules that satisfy the inference mechanism shown in Figures 6.7 (a) to 6.7
(d) are then simply designed as follows:
1. IF actual velocity is smaller THEN inertia matrix is LOW
2. IF actual velocity is normal THEN output is HIGH
3. IF actual velocity is larger THEN output is LOW
From the off-line test, this fuzzy system can easily perform the input-output
mapping. The fuzzy system is then embedded into the overall control scheme for on-
line implementation.
6.3 Simulation
Figure 6.9 shows a Simulink model of the MM-RACKBFAFC.
Figure 6.9: Simulink diagram of the proposed MM-RACKBFAFC
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All of the sub diagrams of blocks in Figure 6.9, that are Input Functions, RAC
Controller plus Inverse Kinematics, Direct Kinematics, Performance Display,
Inverse Dynamics of Mobile Manipulator, and External Disturbances are generally
same with the diagrams of the previous RACAFC scheme which has been
established in Chapters 5 except for the block KBFAFC. Figure 6.10 (a) depicts the
Simulink diagram contained in the KBFAFC block while Figure 6.10 (b) shows the
detailed diagram of the KBF system.
Figure 6.10 (a): Simulink diagram of the block of KBFAFC
Figure 6.10 (b): Simulink diagram of the block of KBF System
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The given task of the MM is to move its platform in a circular motion with a
curvature radius of 10 m, at a velocity of 0.2 m/s (at point F) and the initial heading
angle orientation of π/2.4 rad to the zero angle of the world Cartesian coordinate.
The manipulator is programmed to follow a specified curve track at the right-hand
side of the platform starting from (10.41, 0.35) m of the world Cartesian coordinate.
The initial tip position is set to point (10.55, 0.35) m.
The values of Kp and Kd of the RAC for the AFC schemes have been
obtained previously, that are 004.0450450350350diagKpRACAFC =
and 0017.0320320320320diagKd RACAFC = . These values are consequently
used in the RAC part for all the proposed schemes to ensure a fair comparison can be
made.
6.4 Results and Discussion
All the results obtained from the RACKBFAFC scheme would be compared
to those of RACAFC. The discussion deals with the following headings:
• Effects of Constant Torque Disturbance, Qc
• Effects of Impact Disturbance, Qimp
• Effects of Vibration, Qvib
6.4.1 Effects of Constant Torque Disturbance
As an initial evaluation on the robustness, some constant torque disturbances,
Qc, are introduced to the RACKBFAFC where Qc = [Qclink-1; Qclink-2; Qcwheel-L;
Qcwheel-R] is set as follows:
a. [ ]TQc 5522 −= Nm (high Qc),
b. [ ]TQc 30303030 −= Nm (super high Qc).
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Figures 6.11 (a) to 6.10 (d) show TTE of the arm and body of the
RACKBFAFC versus RACAFC scheme. From the figures, it is obvious that
RACKBFAFC is superior to RACAFC. The change of constant torques disturbance
can be significantly compensated by the KBFAFC even the super-high Qc.
Figure 6.11 (a): TTE of Arm, AFC/ KBFAFC, Qc = [0.2;0.2;0.5;-0.5] Nm
Figure 6.11 (b): TTE of Arm, AFC/ KBFAFC, Qc = [2;2;5;-5] Nm
Figure 6.11 (c): TTE of Body, AFC/ KBFAFC, Qc = [20;20;20;-20] Nm
Figure 6.11 (d): TTE of Arm, AFC/ KBFAFC, Qc = [30;30;30;-30] Nm
6.4.2 Effects of Impact Disturbance
The impact disturbances as in the preceding chapters with additional term of
Qgain as gain are introduced to test the other criteria of robustness of the proposed
scheme. Figures 6.12 (a) and 6.12 (b) show the response at the tip end position for
MM-RACAFC and MM-RACKBFAFC which the impacts are introduced at t = 6.5 s
for the joints, and t = 10 s for the wheels. As can be seen, the error on RACAFC has
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tendency to be larger subjects to the increase of amplitude of impacts. In contrast, the
RACKBFAFC persistently rejects the effect of impacts even at the highest impact
(Qgain = 3). In this case, it can be stated that in responses, the RACKBFAFC is
similarly an adaptive scheme which has persistent robustness.
Figure 6.12 (a): TTE of Arm, AFC/ KBFAFC, Qimp, Qgain = 0.1
Figure 6.12 (b): TTE of Arm, AFC/ KBFAFC, Qimp, Qgain = 0.5
Figure 6.12 (c): TTE of Arm, AFC/ KBFAFC, Qimp, Qgain = 1
Figure 6.12 (d): TTE of Arm, AFC/ KBFAFC, Qimp, Qgain = 3
Assuming the road surface of robot’s workspace has uncertainties such as
holes or bumps then the evaluation on the body deals with the impacts type of
disturbance is also performed. Figures 6.13 (a) to 6.13 (d) show the error at point F
of the body due to the impacts with Qgain = 0.1, 0.5, 1.0, and 3.0.
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Figure 6.13 (a): TTE of Body, AFC/ KBFAFC, Qimp, Qgain = 0.1
Figure 6.13 (b): TTE of Body, AFC/ KBFAFC, Qimp, Qgain = 0.5
Figure 6.13 (c): TTE of Body, AFC/ KBFAFC, Qimp, Qgain = 1
Figure 6.13 (d): TTE of Body, AFC/ KBFAFC, Qimp, Qgain = 3
The results obtained shown in the figures are very clear. The RACKBFAFC
applied to the platform can totally reject the impacts, even at Qgain = 3. The method
to adapt the inertia matrix estimation based on evidences (disturbance existences that
measured from the actual velocity) is proven to be very effective.
6.4.3 Effects of Vibration
The robustness of the proposed scheme is also tested by introducing the
vibration along the trajectory tracking. Figures 6.14 (a) to 6.14 (d) show the effects
of the vibration on the MM-RACKBFAFC at the tip end position.
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Figure 6.14 (a): TTE of Arm, AFC/ KBFAFC, Qvib, Qgain = 0.1
Figure 6.14 (b): TTE of Arm, AFC/ KBFAFC, Qvib, Qgain = 0.5
Figure 6.14 (c): TTE of Arm, AFC/ KBFAFC, Qvib, Qgain = 1
Figure 6.14 (d): TTE of Arm, AFC/ KBFAFC, Qvib, Qgain = 3
As with the impact disturbances, the proposed RACKBFAFC also shows its
superiority in rejecting the vibration at the tip end position. Even at Qgain = 3, the
error is still less than 0.15 mm. The same applies for Qgain = 0.5 and 1.
The effect of vibration on the body is also well compensated by the
RACKBFAFC as shown in Figures 6.15 (a) to 6.15 (d). As can be seen, the steady-
state error of body for all the introduced vibrations is less than 0.03 mm in average.
Specifically, from Figure 6.15 (d), it is obvious that the RACKBFAFC performs
much better than RACAFC in which the error is shown to reduce considerably.
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Figure 6.15 (a): TTE of Body, AFC/ KBFAFC, Qvib, Qgain = 0.1
Figure 6.15 (b): TTE of Body, AFC/ KBFAFC, Qvib, Qgain = 0.5
Figure 6.15 (c): TTE of Body, AFC/ KBFAFC, Qvib, Qgain = 1
Figure 6.15 (d): TTE of Body, AFC/ KBFAFC, Qvib, Qgain = 3
6.5 Conclusion
Three major conclusions can be drawn from the study carried out in this
chapter:
• The procedure of knowledge investigation to knowledge processing performed
in this study is proven very effective to simplify the fuzzy system design. The
procedure is also helpful to design the proper fuzzy system applied as the inertia
matrix estimator. In general, the knowledge that captured within the
investigation, that is actual velocity-inertia matrix relation, is successfully
applied as base to design the knowledge-based fuzzy for the intelligent active
force control of the mobile manipulator.
133
• The design of partial KBF for each of subsystem, that are joints and wheels, is
found very efficient to reduce the mathematical burden and the structure of
fuzzy systems. Thus, the RACKBFAFC can be considered as an effective
practical solution on robust motion control.
• From the simulation, the proposed MM-RACKBFAFC is successfully proven as
a stable and robust motion control. Comparing to the RACAFC, the proposed
scheme is much better in general robot operation including the presence of the
disturbances in the form of pulses impact and vibration.
CHAPTER 7
EXPERIMENTAL MOBILE MANIPULATOR
7.1 Introduction
This chapter describes the practical development of the mobile manipulator.
A complete experimental rig called MMAFCON (Mobile Manipulator AFC ON-line
system) is designed and developed to demonstrate the feasibility and
implementability of the investigated control methods proposed in the theories. The
concept of mechatronics approach in designing the MMAFCON system is especially
highlighted as it involves the full integration of the mechanical, electronics and
computer control disciplines. For the initial stage of the practical implementation of
the proposed schemes we have experimented the RAC and RACAFC. The
experiment on the RAC only scheme is to show the effectiveness of the proposed
simplified coordinates (x, y) and heading angle (φ) of nonholonomic mobile robot
motion control using resolved acceleration control. Based on this then the RACAFC
is experimented to demonstrate the powerful of the AFC scheme. Note that due to the
technical constraints in the rig design such as imprecise mounting and improper
specification of the mechanical, electrical and electronic components including
motors and sensors, the precise tracking by the proposed (and improved) AFC
scheme could not clearly be measured in practice. The experimentation of both the
RACAFC and RACKBFAFC are done with such practical constraints.
135
7.2 Specifications of Mobile Manipulator
Generally, the MMAFCON system comprises both the mobile platform and
two-link robot arms and is composed of the hardware and software components. The
hardware is made up of mechanical, electrical and electronics elements including the
personal computer based control system. The main interface between computer and
the rig is accomplished using two units of the data acquisition card DAS1602. The
software or the driver program is designed using a high level programming language,
i.e., C language. For ease of use, executable files are built into the driver program
and can be executed under the common personal computer disk operating system
(DOS) environment.
The experimental rig developed in this study is constrained by a number of
limitations as follows:
- Types of the motors are actually DC-servomotors with linear
characteristics, however not exactly torque motors as needed.
- For the platform, the accelerometer cannot be mounted on the wheel as in
the simulation due to impossibility to install this wired-type sensor at the
angular side of the wheel.
- It is difficult to keep the weight of the robot, whether totally or on
subsystems, as same as in the simulation, particularly due to the weight of
the cable connection among the PC and robot that should not included to
the total weight.
- The adjustment of center of gravity of the robot is also complicated. To
solve it we adjusted the mounting position of the batteries.
- Frictions, backlash, and imprecise mounting of the rig are considered as
unstructured dynamics and unknown disturbances.
Table 7.1 shows the specifications of the rig that was designed and developed
in this study.
136
Table 7.1: Specifications of the rig
Parameters Mobile Platform Manipulator
Type Differentially-Driven Mobile Robot (left & right)
Two-link Planar Arm
Mass of platform 48 kg Mass of wheel 1 kg (each) Half width of platform 0.4 m Radius of wheel 0.11 m Distance of point G to F 0.3 m Mass of link-1 (plus motor at joint 2) 3.45 kg Length of link-1 0.4 m Length of link-1 from joint-1 to centre of gravity
0.24 m
Mass of link-2 (plus gripper) 4.25 kg Length of link-2 0.38 m Length of link-2 from joint-2 to centre of gravity
0.21 m
Type of Motor joint-1 VEXTA: Motor AXHM450K
Gear GFH4G100
Type of Motor joint-2 VEXTA: Motor AXHM230K Gear GFH2G100
Type of Motor wheel-L VEXTA: Motor AXHM450K
Gear GFH4G50
Type of Motor wheel-R VEXTA: Motor AXHM450K
Gear GFH4G50
The total weight of the mobile manipulator is around 55.70 kg including
batteries with the weight of the manipulator is around 7.7 kg including the gripper.
The length of the manipulator is 40 cm for link-1 and 38 cm for link-2. The distance
between two wheels is 80 cm with the wheel radius of 11 cm.
The isometric view of the mobile manipulator rendered from the
AUTOCAD® drawing is shown in Figure 7.1 (a), while the actual mobile
manipulator and its current end-effector are shown in Figures 7.1 (b) and 7.1 (c)
respectively.
137
Figure 7.1 (a): Isometric view of the mobile manipulator
Figure 7.1 (b): A photograph of the mobile manipulator in action
Figure 7.1 (c): Proposed gripper attached to the manipulator
In Figure 7.1 (c), the gripper that is attached to tip position is operated to
grasp and move the object/load with maximum of 1 kg. The small window at the
right corner in Figure 7.1 (b) shows the first development of the robot in which the
grasper/gripper has been improved by redesigning the mechanical parts and replacing
the motor with the more sophisticated ones (VEXTA Motor). Figure 7.1 (c) shows
the current gripper design.
7.3 Personal Computer (PC) Based Controller
The controller of the mobile manipulator developed in this study is composed
of two types, i.e. PC controller supported by DAS1602 interface cards, and
138
Embedded Controller System based on a Microchip Peripheral Interface Controller
PIC16F877. These controllers can be selectively operated by setting the connectors
attached at the robot’s body. Figure 7.2 shows the outline of the experiment
conducted for the PC based controller that is supported by two units of data
acquisition cards DAS1602® manufactured by Keithley® Inc. The schematic diagram
of the PC based controller of the mobile manipulator is shown in Figure 7.3.
Mobile Platform
Gripper
Manipulator system
castor
Front wheels (nonholonomics)
PC Pentium III (with ISA slot)
2 units DAS1602 (inside)
Parallel cables (8 × 16lines)
MMH852.EXE is executed here.
Mobile Manipulator system
Figure 7.2: An experimental set-up for the PC-based controller
Figure 7.3: Schematic diagram of the PC based controller
139
Basically, the design of PC based controller must be able to organize all of
the input and output functions of the mobile manipulator control as well as in the
simulation. In total, the controller has four channels of parallel input functions for
position variables, 12 channels of analog input functions for the velocity,
acceleration and current sensors, and four channels of analog output functions for the
actuators. For the position sensor, a frequency to voltage converter is applied to
convert the pulses signals of the output of the rotary encoder to a linear analog signal
for the purpose of measurement using the DAS1602 card. The motors used in the
robot are DC servomotors that have embedded motor driver independently. The
motor is driven by analog signal through the input of the driver which connects to the
analog output of the DAS1602. Note that the motor moving direction must be driven
by 1-bit digital output particularly, logic 1 for clock-wise, and logic 0 for counter-
clock-wise direction.
7.3.1 Computer and Data Acquisition System (DAS) Card
The computer that is used as the controller is based on Pentium III PC –
1GHz with at least two units of EISA (Extended Industrial System Association) slots
on the CPU board for the DAS1602 cards connection. Figure 7.4 shows the mounting
of DAS1602 cards (two units) to the EISA slots.
It is noted that the power consumption must be sufficiently supplied by the
PC power supply system. One card basically needs 1 to 3 Ampere when it runs. For
the purpose of experiments, the analog input of ADC (Analog to Digital Converter)
of the cards is set to bipolar function due to the outputs of sensors have analog
voltage signals. While the analog output of DAC (Digital to Analog Converter) is set
to unipolar function due to the motors must be commanded using unipolar voltage.
The motors’ moving direction is driven by the particular digital output that is one bit
for each motor. The complete specification of the DAS1602 card can be found in the
datasheet (Computer Boards, 1998).
140
Figure 7.4: Two units of DAS1602 cards on the CPU Board
7.3.2 Frequency to Voltage Converter (f/V) Circuits
The motors used in the mobile manipulator are DC servomotor that has built
in speed sensor with pulse signals output. Actually we can directly connect the speed
sensor output to the digital input of the DAS1602 card. Consequently, the sensor
output in pulses form must be converted to linear analog voltage in the program.
However, it will be costly in computation and is time consumable.
To avoid the above problems, we implement a frequency to voltage converter
as signal conditioning to the sensor so that the speed or velocity measurement can be
performed through the analog input of the ADC of the DAS1602. Converting the
sensor output to the linear analog signal basically can simplify the sensors reading
processes in the program by only single instruction that is to read data from ADC. In
contrast, pulses signal need to be converted using counters or similar function in
programming or by functioning the programmable counter (hardware) of the
interface. We use an IC LM2907 as converter for each of velocity signal of the
motor. Figure 7.5 shows the (f/V) circuit.
141
20K
100K 0.1 1µF/25V
10µF /50V
7809
LM2907 f/V Converter
10K 25Ω 1W
+24V
Pulses from Speed sensors
Vout
CHARGE PUMP
+
-
+
-
0.01
VR
Figure 7.5: Frequency to Voltage Converter circuit
The IC LM2907 needs +9V supply system to work, while the robot system
voltage is ±12V or ±24V. Therefore, an additional voltage regulator should be added
to the circuit, as shown in Figure 7.5. The sensitivity of conversion can be adjusted
through the variable resistor VR. It is highlighted that the sensor’s wiring
connections should use shielded (coaxial) cable to protect the signal from
interferences or electromagnetic signals from the environments.
7.3.3 Rotary Encoder Circuits using HCTL2000
Figure 7.6 shows the complete circuit diagram of the signal conditioning
system of the rotary encoder used in the robot controller. In the figure, the rotary
encoders with function of CHA and CHB as the common signals are managed in
which the four encoders can be read by the processor in real-time. It means the
processor should use the effective way to read the position of each motor anytime
when the sensor (position) reading is needed. Therefore the circuit is designed as
particular section that can communicate to the processor using the specific bus
connections. The bus consists of address bus (Port A of 82C55), data bus (Port B of
82C55), and handshaking signals (Port C of 82C55) as shown in the figure.
In Figure 7.6, CHA and CHB are Schmitt-trigger inputs which accept the
outputs from a quadrature encoded source, such as the incremental optical shaft
encoder. Two channels, A and B, nominally 90 degrees out of phase, are required.
142
designed by Pitowarno, E.
© 2004
9
OE
10 11 12 13 14 15 1
SEL RST
8 2
7
8
Rotary Encoder
MR
CH A
CH B
Vcc +5V
HC
TL 2
000
4 3 5
Vcc +5V
16 0.1
74HCT245
DIR
‘1’
OE
Clock
9
OE
10 11 12 13 14 15 1
SEL RST
8 2
7
8
Rotary Encoder
ML
CH A
CH B
Vcc +5V
HC
TL 2
000
4 3 5
Vcc +5V
16 0.1
74HCT245
DIR
‘1’
OE
Clock
9
OE
10 11 12 13 14 15 1
SEL RST
8 2
7
8
Rotary Encoder
M1
CH A
CH B
Vcc +5V
HC
TL 2
000
4 3 5
Vcc +5V
16 0.1
74HCT245
DIR
‘1’
OE
Clock
9
OE
10 11 12 13 14 15 1
SEL RST
8 2
7
8
Rotary Encoder
M2
CH A
CH B
Vcc +5V
HC
TL 2
000
4 3 5
Vcc +5V
16 0.1
74HCT245
DIR
‘1’
OE
Clock
PC7-PC4
PC3-PC0
PB7-PB0
PA7-PA0
To PPI 82C55 of
PIC16F877 based controller
or PC’s DAS1602
based controller
CN3
Z
Z
Z
Z
Figure 7.6: HCTL2000 based Rotary Encoder Signal Conditioner
The quadrature decoder samples the outputs of the CHA and CHB. Based on
the past binary state of the two signals and the present state, it outputs a count signal
143
and a direction signal to the internal position counter. Then the data that were saved
in the counter can be read by the processor anytime.
The processor needs to handshake to the encoder circuit when the reading is
performed. Firstly, the processor sends SEL signal to the address of appropriate
encoder. Then, OE is sent during the active SEL. From this point, the addressed
encoder circuits will prepare a latched signal (latest data) at the data bus to ensure the
data is valid. Now, the processor can safely fetch up the data from the bus.
7.3.4 Signal Conditioning Interfaces
Figures 7.7 and 7.8 show some views of the circuit boards containing the
signal conditioners for all sensors and actuators. These boards were designed in such
a way the wiring connection could easily be maintained for the purpose of debugging
the program. Note that the connectors J-1 and J-2 in Figures 7.6 and 7.7 must be
disconnected when the robot is controlled by the embedded controller system to
ensure no signals interference among the PC and the embedded controller.
Figure 7.7: Signal conditioning interface for the mobile platform
144
Figure 7.8: Signal conditioning interface for the manipulator
7.3.5 Programming Design
The program developed for the PC based controller is written in C. Essential
program modules can be seen in Appendix C. To ensure a faster access time when
the on-line feedback control program is running, the program is designed to run in
the DOS (Disk Operating System) mode. It is known that all of the interrupt system
programs in the Windows O/S based will be terminated (cancelled) when the PC is
run under DOS. The PC-based program is developed with a real-time graphical
display for convenience to the user. This feature is named RTM (Real Time
Monitor). In the program development and testing at the initial stage, it is found that
the quality of the power supply (voltage) to the system is very crucial. Note that the
robot uses batteries to power the system. When the voltage or current of the batteries
is low, the voltage reference used in the sensory-based measurement is affected, so
that the sensor data is invalid. Consequently, the sensor must be recalibrated each
time the power system becomes insufficient or weak. If not, the control parameters
must be retuned to recover this adverse condition.
145
Therefore an additional procedure or function in a form of a computer
program need to be designed to initially calibrate the power system before the main
program is executed. The modified program is an executable file, MMH852.EXE in
which it is able to readjust and recalibrate the sensory systems dynamically and
automatically whenever the program is executed. Hence, the user can observe and
evaluate the reference voltage of sensory system (shown as the ADC output value)
that may exhibit undesirable change when the robot starts to run. The displayed value
was then automatically used as reference value for computation in the program. From
the experiments it is obtained that this procedure can substantially compensate the
effects of the power system instability. Figure 7.9 shows the display on the computer
screen when the calibration procedure is executed.
Figure 7.9: Display window of the calibration process through the program MMH852.EXE
For convenience in monitoring the robot operation and program debugging,
the display is designed as a real-time graphical monitoring system. A sample of the
display captured from the PC monitor is shown in Figure 7.10. In the figure, the left
side is the real-time display of all sensor readings installed in the robot system. The
middle portion of the graph shows the trace of the trajectory that is generated during
the robot movement. The green line is the desired trajectory while the red one is the
actual. The generated errors can also be monitored instantly but crudely (not scaled)
146
during the operation. The window at the bottom-right corner is the display for the
selected control parameters, desired track and the initial conditions. In addition, the
display is developed for three window settings related to the RAC, RACAFC, and
RACKBFAFC schemes considered in the study.
Figure 7.10: A sample of the display captured from the PC screen
7.4 Embedded Controller using PIC16F877
Figure 7.11 shows an outline of the experimental set-up for one of the earlier
versions of the prototype of the complete autonomous mobile manipulator that is
controlled by an embedded controller using PIC16F877 as the main CPU.
CPU: PIC17F877 I/O(+extra): 4ch analog output, 2ch PWM
outputs, more than 24-bits digital I/O HCTL2000 based rotary encoder circuits f to V converter for velocity sensors Monitor: LCD LXC2425STY (24 × 2) Keypad: 4 push botton Programming: C using Hitech C Cross
Compiler Battery: (2 × 7.5A)12V, (1 × 12A)12V
Autonomous MobileManipulator System
Program PICMM13.HEX is executed here
Figure 7.11: A descriptive diagram of the autonomous mobile manipulator
147
The microcontroller PIC 17F877 is selected as the embedded controller of the
mobile manipulator in this study. The considerations are based on the following
specifications (Microchip, 2001):
• high performance RISC CPU in fully static design at low price
• high speed CMOS FLASH/EEPROM technology
• low-power consumption at maximum 25 mA
• up to 8K x 14 words of FLASH Program Memory
• up to 368 x 8 bytes of Data Memory (RAM)
• up to 256 x 8 bytes of EEPROM Data Memory
• In-Circuit Serial Programming⎢ (ICSP) via two pins
• only 35 single word instructions to learn
• all single cycle instructions except for program branches which are two cycle
• wide operating voltage range: 2.0V to 5.5V
• many other advantages as described in the datasheet.
Figure 7.12 shows pins configuration of PIC16F877. This IC has five ports,
namely, RA5-RA0, RB7-RB0, RC7-RC0, RD7-RD0, and RE2-RE0. Pins of RA5, RA3,
RA2, RA1, RA0, RE2, RE1, and RE0 can be initialized as analog input port at 10-bit
resolution. Thus, there are eight channels of analog input that can directly be
connected to the sensors.
123456789
1011121314
2827262524232221
151617181920
293031323334353637383940MCLR/Vpp
RA0/AN0RA1/AN1
RA2/AN2/Vref-RA3/AN3/Vref+
RA4/T0CK1RA5/AN4/SSRE0/RD/AN5RE1/WR/AN6RE2/CS/AN7
VddVss
OSC1/CLKinOSC2/CLKout
RC0/T1OSO/T1CKIRC1/T1OSI/CCP2
RC2/CCP1RC3/SCK/SCL
RD0/PSP0RD1/PSP1
RB7/PGDRB6/PGCRB5RB4RB3/PGMRB2RB1RB0/INTVddVssRD7/PSP7RD6/PSP6RD5/PSP5RD4/PSP4RC7/RX/DTRC6/TX/CKRC5/SDORC4/SDI/SDARD3/PSP3RD2/PSP2
16F877
Figure 7.12: Pins configuration of PIC16F8771
1 PIC16F877 is trademark of Microchip Inc.
148
The microcontroller can be programmed using a high level language (e.g. C)
so that the equations derived from the theoretical investigation could be easily
rewritten in the program. Compiling the program can be done using Hitech C Cross
Compiler® from Hitech®2 Software.
7.4.1 Embedded Controller Circuit
By considering the input/output configuration as shown in Figure 7.12, the
embedded controller was then designed as shown in Figure 7.13. The sensors were
directly connected to the chip through the connector CN1, except for the rotary
encoders. In this case, we use an IC PPI (Programmable Peripheral Interface) 8255A
as the interface of the encoder to the PIC. As can be seen in the figure, the PPI8255A
is designed such that the PIC can communicate with the encoder using the specific
bus connection through the connector CN2. Note that due to the limitation of the
analog inputs of the PIC which has only eight channels, whereas the robot system
needs 12 channels, then four channels (supposedly two channels for the current
sensors and two channels for the accelerometers for the AFC function of the
platform) are not connected. Consequently, the application of AFC is limited to the
manipulator section only.
To drive the actuator system, an IC DAC0808 was used to perform the
analog output and 1-bit digital output for commanding the moving direction. In this
case, an IC 74HC377 was employed as the multiplexer to address the target motor. In
total, there exists four channels of analog output to drive the actuator systems.
A mini display system was also designed using LCD (liquid crystal display)
module, LXC2425STY that has two lines and 24 characters for each line. In this
display, the status of the robot operation can be monitored. Figure 7.13 shows the
complete circuit diagram of the embedded controller system for the autonomous
mobile manipulator.
2 Hitech C Cross Compiler is trademark of HI-TECH Software Pty Ltd., Australia.
149
RA
7-R
A0
RB
7-R
B0
RC
7-R
C0
RA7-RA0 RB7-RB0 RC7-RC0 RD7-RD0
RD
7-R
D0
RA2 RA3
RS E
D7-D4 RB3-RB0
74HCT138
74HCT377
74HCT377
74HCT377
74HCT377 DAC0808
DAC0808
DAC0808
DAC0808
LCD LXC2425STY
Motor Driver M2
Motor Driver M1
Motor Driver ML
Motor Driver MR
Q7-Q0
Q7-Q0
Q7-Q0
Q7-Q0 Analog Out
AnalogOut
Analog Out
Analog Out
CP
CP
CP
CP
E
E
E
E
Y2
Y3
Y1
Y0
Y3-Y0
C B A
RB7 RB6
D7-D0
D7-D0
D7-D0
D7-D0
RB5
RB5
RB5
RB5 RC7
RC6
RC5
RC4 DIR
DIR
DIR
DIR
Vin
Vin
Vin
Vin
G1 G2A G2B
10
1
PIC 16F877
1
2
3
4
VEXTA: Motor AXHM450K Gear GFH4G50
VEXTA: Motor AXHM450K Gear GFH4G50
VEXTA: Motor AXHM450K Gear GFH4G100
VEXTA: Motor AXHM230K Gear GFH2G100
Rθ&
Lθ&
1θ&&
2θ&1θ&2θ&&
I1 I2
RA2 RA1
RA2 RA3 RA5 RE0 RE1 RE2
A1 A0
CS
RB1 RB0
RB2
RC0 RC3
RDCPWR
PA3 PA2 PA1 PA0
+5V
GND
PC5 PC4 PC1 PC0
OE1 SEL1
OE2 SEL2
RST1
RST2Z1 Z2
PPI82C55
PA7-PA0
PC7-PC0
PB7-PB0
D7 D6 D5 D4 D3 D2 D1 D0
To HCTL2000 Section
(rotary encoder)
CN2
from Sensors
CN1
designed by Pitowarno, E.
© 2004
D7-D0
Replacable connector (can be used by PC)
Figure 7.13: Circuit diagram of PIC16F877 based controller
150
7.4.2 Controller Board
Figures 7.14 (a) to (d) show the autonomous mobile manipulator, the
mounting of the embedded controller, the PIC 16F877 based embedded controller
and the power supply unit for the embedded controller.
Figure 7.14 (a): A view of the Autonomous Mobile Manipulator
Figure 7.14 (b): The mounting of the embedded controller
Figure 7.14 (c): The PIC 16F877 based embedded controller
Figure 7.14 (d): Power Supply unit for the embedded controller
The controller, as seen in Figure 7.14 (c), is designed in one board system so
that the wiring system could be minimized. The connectors attached on the board can
be easily connected to the sensor and actuator systems using flat cables.
151
7.5 Experimental Results and Discussion
The experimental result highlighted in this discussion is based on the PC-
based controller. Using PC-based controller, the measurement of the actual
conditions of the robot operation is automatically performed by the program and the
data is automatically recorded in the hard disk of the PC after program execution. In
the embedded system, the data recording cannot be performed due to the limitation
of the memory. As mentioned earlier, the R/W (read/write) memory capacity of the
PIC is 2 Kilobytes only.
It is desired that the robot task is to move its platform in a circular motion
with a curvature radius of 1.5 m, at a velocity of 0.2 m/s (at point F) and the initial
heading angle orientation of 0 rad to the zero angle of the world Cartesian
coordinate. The friction, backlash and imprecise mounting of the elements in the rig
maybe considered as unstructured dynamics and unknown disturbances. Note that in
this experiment, the AFC and KBFAFC are implemented to the manipulator only due
to the use of wired-sensor type of the accelerometers.
Figures 7.15 and 7.16 show the results for the RACAFC and RACKBFAFC
schemes respectively.
Figure 7.15: Experimental results of the RACAFC scheme
152
Figure 7.16: Experimental results of the RACKBFAFC scheme
From the instant visualization as shown in the window of Track Error in
Figures 7.15 and 7.16, it can be deduced that the RACKBFAFC performs better than
the RACAFC counterpart. The actual tracking errors at the tip position for both
schemes can be seen in Figure 7.17 where the graphs are redrawn from the recorded
data after program execution.
Figure 7.17: Tracking errors of the arm in the experiment of RACAFC and RACKBFAFC schemes
153
Figure 7.18 depicts the actual acceleration at the joints for the RACAFC and
RACKBFAFC schemes, while the applied current of the motors can be seen in
Figure 7.17. As can be seen, the actual acceleration in the experiment is very
sensitive and tends to be spiky. It is probably due to the backlash of gearbox of the
motors at the joints. It is highlighted that from the current signals, it can be deduced
that there seems to be nonlinearity in the motors characteristic. In the range of around
±0.3A it seems the moving direction is abruptly changed. In fact, after the thresholds,
the motors smoothly move and track the trajectory. It may be also due to the
backlash of the gears and the fact that the motors driver circuit is nonlinear within the
range of currents. It is reasonable due to the motor VEXTA used in the experiment is
actually a brushless motor that needs offset current to start to move.
Figure 7.18: Actual acceleration at
the joints, RACAFC and RACKBFAFCFigure 7.19: Actual motor currents at
the joints, RACAFC and RACKBFAFC
7.6 Conclusion
From the experiments conducted, a number of conclusions can be drawn and
are listed as follows:
• The autonomous mobile manipulator was successfully designed and
developed in this study in the form of a working prototype but with very
limited memory for programming.
154
• The experiments show the successful implementation of the AFC scheme in
mobile manipulator motion control considering some practical constraints.
• In the experiment, the RACKBFAFC has been proven to perform better than
the RACAFC. This is in line with the results obtained through the simulation
study and hence validates the theoretical aspect of the research. However,
further investigation has to be carried out by introducing other forms of
disturbances and trajectories to enhance the system performance, particularly,
in terms of robustness, stability and accuracy.
CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS
8.1 Conclusion
It can be summarized that the specific objective of the project has been
satisfactorily achieved in that an ultimate working prototype of an intelligent mobile
transporter with AFC capability operating in an appropriate ‘factory’ setting was
successfully designed and developed. Both theoretical and practical aspects of the
research were rigorously and systematically executed.
The simulation study on the mobile robot system was performed considering
various AFC-based schemes with a number of intelligent elements and disturbances
incorporated into the schemes - all pointing towards the same direction (conclusion),
i.e. all producing the expected results which indeed verify the robustness and
effectiveness of the AFC algorithm. The RAC knowledge-based fuzzy AFC
(RACKBFAFC) scheme was particularly very efficient and accurate in performing
the trajectory tracking tasks under various operating and loading conditions. A new
method of tuning the estimated inertia matrix of the mobile robot system through
KBF technique was realized.
The practical system was successfully developed in the form of a working
prototype mobile manipulator employing a number of control schemes that are
theoretically defined in the earlier chapters. Only RAC, RACAFC and
RACKBFAFC schemes were realized and implemented into the prototype by way of
156
rigorous programming, interfacing and control. The results obtained from the
experiments do complement and ‘tally’ with those of the theoretical (simulation)
counterparts implying that the schemes were successfully validated even though it
was found that the experimental findings were rather crude and much lower in
accuracy, obviously due to a number of physical constraints. Indeed, a complete
mechatronic approach and design was fully utilised and implemented here.
One of the innovative features that is incorporated into the research is the
application of virtual reality (VR) technique to the mobile manipulator that enables
user to visualise the operation of the system in different perspective. The simulator is
tested and evaluated considering a factory layout in the form of computer integrated
manufacturing (CIM) environment. A collision avoidance algorithm was successfully
implemented into the simulator making it more autonomous and intelligent.
8.2 Recommendations for Future Works
A number of recommendations for future works is listed as follows:
• Perform a rigorous stability analysis of the mobile manipulator with
various AFC-based schemes.
• Simulate system using other forms of operating and loading conditions to
further investigate the system robustness and accuracy in performing its
tasks. This may include different trajectories (paths), terrains, velocities,
payloads, tasks and other forms of external disturbances.
• Add more intelligence to the system be it through software program
(incorporating other articicial intelligence (AI) techniques) or hardware
by way of using intelligent (or smart) sensors and electronics.
• Solve some of the current problems related to physical hardware
constraints such as appropriate mounting of sensors and actuators and
also using more accurate sensors.
157
• Further practical experiments need to be carried out to obtain other useful
characteristics or behaviours of the mobile manipulator.
• A number of end-effectors (grippers or tools) can be designed, developed
and installed to the manipulator. This may be done in total isolation of the
system at the initial stage and may involve the use of different controller
(e.g. PLC, microcontroller or even PC-based control). However,
synchronisation need to be done to ensure that the overall system runs
efficiently.
• The mobile manipulator can be further tested in actual manufacturing
environment to perform specific tasks.
• A self charging gadget for the battery can be designed and added to the
system to enhance its innovative feature.
• The VR application can be improved to take into account more immersive
features and different work settings/environments.
158
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Appendix A
Notes on Heuristic Search Algorithms
A.1 Graph Searching Algorithm
Through a priori generated search space, a graph searching algorithm is required for the searching of a sequence of collision-free actions that will lead the mobile robot to the destination point with minimum cost. A number of graph searching algorithms can be applied for the findings of the collision-free nodes, namely breadth first algorithm, depth first algorithm, Dijkstra’s method, Best-First-Search (BFS) algorithm, and A* heuristic algorithm. In this research, comparison has been conducted between Dijktra’s method, Best-First-Search (BFS) algorithm, and A* heuristic algorithm. Generally, Dijkstra’s method works in progressive stages to calculate the total cost of the shortest path from a single vertex to all other vertices [71]. The algorithm for Dijkstra’s method is as shown in Figure 3.8. The graph searching begins with the initialization of the search. The total cost, F for initial vertex and all other vertices are set to 0 and infinity respectively. After the initialization of the search, the current vertex, V is marked as visited. The total cost for all the vertices adjacent to V, Fchild is then adjusted through the summation of the total cost of V, FV with the cost of the edge to the adjacent vertex, FV-child. If the total cost for the adjacent vertex is less than the previously stored total cost, then the total cost for the child vertex is adjusted, or else it is left unchanged. All the vertices are then determined for their status. Vertex with the least total cost and unvisited will be selected as V, and the process is iterated until all the vertices are visited.
Figure A.1: Flow chart of Dijkstra’s method
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BFS algorithm works in a similar way as Dijkstra’s method except that it practices certain heuristic features in the selection of successors. Instead of selecting the vertex closest to the starting point as shown in Dijkstra’s method, BFS algorithm tends to choose heuristically the vertices which are closest to the goal as the successors. In brief, BFS is not guaranteed to find a shortest path as Dijkstra’s method does, but BFS requires less computation time in solving the graph searching because fewer vertices in the graph are explored (LaValle, 2004). However, BFS is ‘greedy’ in the sense that it will always moves towards the goal although the selected successors are not on the right path. Therefore, in order to compromise the best features of these two algorithms, i.e. Dijkstra’s method and BFS algorithm, A* heuristic algorithm has been introduced to search for the most optimum path. In general, heuristics are criteria, methods or principles which are adopted for the decision making in order to generate the most effective goal achieving approach (Pearl, 1984). The main purpose for the application of heuristics are to compromise between two requirements: to make the decision making rules simpler and at the same time discriminate correctly between good and bad choices. Usually, AI solvers employ heuristics in two basic situations (Luger, 2002), where
(i) the problem may not have an exact solution due to inherent ambiguities in the
problem statement or available data. (ii) the problem may have an exact solution, but the computational cost of finding for
the solution may be prohibitive in terms of excessive computational times or limited computational resources.
In this research, A* heuristic algorithm, which has actually combined the best features of
depth-first and Dijkstra’s algorithms has been applied for the searching of the collision-free path. The A* heuristic algorithm is shown as follows:
1. Put the start node Ns on Open List 2. If Open List is empty, exit with failure. 3. Remove from Open List and place on Closed List a node Ni for which the cost
function, f(Ni) is minimum. 4. If Ni is a goal node NG, exit successfully with the solution obtained by tracing back
the pointers from Ni to Ns. 5. Otherwise expand Ni, generating all its successors, and attach to them pointers back
to Ni-1. For every successor Ni+1: 5.1 If Ni+1 is not on Open List or Closed List, the heuristic function, h(Ni+1) is
estimated before the total cost of the action from Ni to Ni+1 is obtained. 5.2 If Ni+1 is already on Open List or Closed List, its pointer is directed along
the path which yields the lowest g(Ni+1). 5.3 If Ni+1 requires pointer adjustment and it is found on Closed List, then it is
reopened. 6. Go to step 2
The flow chart of the A* heuristic search algorithm is illustrated in Figure A.1. From step 5.1,
the total cost, f(Ni+1) is calculated as follows: f(Ni+1) = g(Ni+1)+h(Ni+1) , and (A.1) g(Ni+1) = g(Ni) + c(Ni,Ni+1) (A.2) In equation (A.2), c(Ni,Ni+1) is the cost of action moving from Ni to Ni+1. In this research, the
heuristic function h(Ni+1) is estimated from the Euclidean distance between the successor, Ni+1 and the goal, NG. The estimation of h(Ni+1) is expressed as follows:
( ) ( ) ( )21
211 NGNiNGNii yyxxNh −+−= +++ (A.3)
167
Figure A.3: Flow chart of the A* heuristic search algorithm
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Appendix B
Computer Program for the Development of Virtual Environment (VE)
#include "matlab.h" #include "simulator.h" #include "wt.h" #include "Model.hpp" #include "Astar.hpp" #include "Solution.hpp" #define MapHeight 164 #define MapWidth 200 Solution *Final=new Solution; //Main Program int main() //Unvierse setup WTuniverse_new(WTDISPLAY_DEFAULT,WTWINDOW_DEFAULT); WTuniverse_seteventorder(4,event_array); WTuniverse_setbgrgb(20,10,60); root=WTuniverse_getrootnodes(); WTlightnode_load(root,"lights"); //Building up the scene MainWin=WTuniverse_getwindows(); WTwindow_setposition(MainWin,0,0,1280,974); camera1=WTuniverse_getviewpoints(); mouse=WTmouse_new(); mouselink=WTmotionlink_new(mouse,camera1,WTSOURCE_SENSOR,
WTTARGET_VIEWPOINT); TopView=WTviewpoint_new(); //Setting viewpoint for each window WTwindow_setviewpoint(MainWin,camera1); //Repositioning the viewpoint for main window pos[0]=-750.0f; pos[1]=-100.0f; pos[2]=300.0f; WTviewpoint_setposition(camera1,pos); dir[0]=0.0f; dir[1]=0.0f; dir[2]=1.0f; WTviewpoint_setdirection(camera1,dir); //Repositioning the viewpoint for Orthographic view posTop[0]=-748.0f; posTop[1]=-904.0f; posTop[2]=617.0f; WTviewpoint_setposition(TopView,posTop); dir[0]=0.0f; dir[1]=1.0f; dir[2]=0.0f; WTviewpoint_setdirection(TopView,dir); //Adjusting the sensitivity of mouse WTsensor_setsensitivity(mouse,(float)0.01*WTnode_getradius(root)); //Setting Up for the Virtual Environment SceneGraph(); WTuniverse_setrendering(WTRENDER_BEST); WTuniverse_setactions(Actions);
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WTkeyboard_open(); WTuniverse_ready(); WTuniverse_go(); WTuniverse_delete(); return 0; ; //Function void SceneGraph(void) //Grouping all facilities into a group node facility=WTgroupnode_new(root); SepCup1=WTsepnode_new(facility); cupboard1=WTmovnode_load(SepCup1,"cupboard1.3ds",1.0f); pos[0]=0.0f; pos[1]=0.0f; pos[2]=182.0f+160.0f; WTnode_settranslation(cupboard1,pos); WTnode_axisrotation(cupboard1,Y,(float)3.142,WTFRAME_LOCAL); SepCup2=WTsepnode_new(facility); cupboard2=WTmovnode_load(SepCup2,"cupboard2.3ds",1.0f); pos[0]=0.0f; pos[1]=0.0f; pos[2]=90.0f+377.0f; WTnode_settranslation(cupboard2,pos); WTnode_axisrotation(cupboard2,Y,(float)3.142,WTFRAME_LOCAL); SepCup3=WTsepnode_new(facility); cupboard3=WTmovnode_load(SepCup3,"cupboard3.3ds",1.0f); pos[0]=-46.0f; pos[1]=0.0f; pos[2]=92.0f+891.0f; WTnode_settranslation(cupboard3,pos); WTnode_axisrotation(cupboard3,Y,(float)1.571,WTFRAME_LOCAL); instance=WTmovnode_instance(SepCup3,cupboard3); pos[0]=-46.0f; pos[1]=0.0f; pos[2]=92.0f+983.0f; WTnode_settranslation(instance,pos); WTnode_axisrotation(instance,Y,(float)1.571,WTFRAME_LOCAL); SepChair=WTsepnode_new(facility); chair=WTmovnode_load(SepChair,"chair.3ds",1.0f); pos[0]=-56.0-300.0f; pos[1]=0.0f; pos[2]=60.0f+420.0f; WTnode_settranslation(chair,pos); WTnode_axisrotation(chair,Y,(float)1.571,WTFRAME_LOCAL); Create_Instances(SepChair,chair,pos,5,4,56,60,1.571); SepCom=WTsepnode_new(facility); computer=WTmovnode_load(SepCom,"computer.3ds",1.0f); pos[0]=-47.0f; pos[1]=0.0f; pos[2]=64.0f+497.0f; WTnode_settranslation(computer,pos); WTnode_axisrotation(computer,Y,(float)1.571,WTFRAME_LOCAL); Create_Instances(SepCom,computer,pos,1,2,0,170,1.571); SepWash=WTsepnode_new(facility); washplace=WTmovnode_load(SepWash,"washplace.3ds",1.0f); pos[0]=-92.0f-404.0f; pos[1]=0.0f; pos[2]=0.0f+1166.0f; WTnode_settranslation(washplace,pos); WTnode_axisrotation(washplace,Y,(float)0.0,WTFRAME_LOCAL); SepRobTab=WTsepnode_new(facility); RobTab=WTmovnode_load(SepRobTab, "RobTab.3ds", 1.0f); pos[0]=-1000.0f; pos[1]=0.0f; pos[2]=120.0+112.0f; WTnode_settranslation(RobTab,pos); WTnode_axisrotation(RobTab,Y,(float)3.142,WTFRAME_LOCAL); SepRob1=WTsepnode_new(facility); Robot1=WTmovnode_load(SepRob1, "robot1.3ds", 1.0f); pos[0]=-10.0-1000.0f; pos[1]=-75.0f; pos[2]=212.0f; WTnode_settranslation(Robot1,pos); WTnode_axisrotation(Robot1,Y,(float)-1.5708, WTFRAME_LOCAL); SepRob2=WTsepnode_new(facility);
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Robot2=WTmovnode_load(SepRob2, "robot2.3ds", 1.0f); pos[0]=-20.0-1080.0f; pos[1]=-75.0f; pos[2]=112.0f; WTnode_settranslation(Robot2,pos); WTnode_axisrotation(Robot2,Y,(float)0.0,WTFRAME_LOCAL); SepRob3=WTsepnode_new(facility); Robot3=WTmovnode_load(SepRob3, "robot3.3ds", 1.0f); pos[0]=-20.0-1240.0f; pos[1]=0.0f; pos[2]=20.0+472.0f; WTnode_settranslation(Robot3,pos); WTnode_axisrotation(Robot3,Y,(float)1.5708,WTFRAME_LOCAL); SepCnc1=WTsepnode_new(facility); Cnc1=WTmovnode_load(SepCnc1, "cnc1.3ds", 1.0f); pos[0]=-1200.0f; pos[1]=0.0f; pos[2]=300.0f; WTnode_settranslation(Cnc1,pos); WTnode_axisrotation(Cnc1,Y,(float)0.5236,WTFRAME_LOCAL); SepCnc2=WTsepnode_new(facility); Cnc2=WTmovnode_load(SepCnc2, "cnc2.3ds", 1.0f); pos[0]=-1200.0f; pos[1]=0.0f; pos[2]=680.0f; WTnode_settranslation(Cnc2,pos); WTnode_axisrotation(Cnc2,Y,(float)3.142-0.5236f,WTFRAME_LOCAL); SepConveyor=WTsepnode_new(facility); Conveyor=WTmovnode_load(SepConveyor,"Conveyor.3ds", 1.0f); pos[0]=-300.0-820.0f; pos[1]=0.0f; pos[2]=510.0+262.0f; WTnode_settranslation(Conveyor,pos); WTnode_axisrotation(Conveyor,Y,(float)1.5708,WTFRAME_LOCAL); SepCim=WTsepnode_new(facility); Cim=WTmovnode_load(SepCim, "cim.3ds", 1.0f); pos[0]=1.0f; pos[1]=0.0f; pos[2]=0.0f; WTnode_settranslation(Cim,pos); ; void Create_Instances(WTnode *root, WTnode* base, WTp3 &pos, int numX, int numY, int DistX, int DistY, double rotation) WTp3 p; WTp3_init(p); for(int x=0; x<numX; x++) for(int y=0; y<numY; y++) if((x==0) && (y==0)) p[0]=pos[0]; p[1]=pos[1]; p[2]=pos[2]; continue; instance=WTmovnode_instance(root,base); p[2]=p[2]+DistY; WTnode_settranslation(instance, p);
WTnode_axisrotation(instance,Y,(float)rotation, WTFRAME_LOCAL);
p[2]=pos[2]-DistY; p[0]=p[0]-DistX; ; void Actions(void) short key;
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key=WTkeyboard_getkey(); switch(con) case 0: break; case 1: unsigned int n=0; unsigned char R=0, G=0, B=0, A=0; //Windows image capture unsigned char image[MapWidth*MapHeight*4]; int temp[MapWidth*MapHeight]; //Capturing for the Top View
WTwindow_getimage(Top,0,210,MapWidth,MapHeight, image);
n=0; for(i=0; i<MapHeight; i++) for(unsigned int j=0; j<MapWidth; j++) R=image[n]; n++; G=image[n]; n++; B=image[n]; n++; A=image[n]; n++; if((R==161) && (G==161) && (B==161) &&
(A==255)) temp[i*MapWidth+j]=1; else temp[i*MapWidth+j]=9; ; //Manipulation of Windows for VE WTwindow_delete(Top); Path_Planning(temp); SepMobileR=WTsepnode_new(facility); MobileR=WTmovnode_load(SepMobileR, "MobileR.3ds",
1.0f); WTnode_axisrotation(MobileR,Y,(float)1.5708, WTFRAME_LOCAL);
Loop=0; con=2; break; case 2: Loop++; if(Loop==1) timespan=0; timespan=timespan+0.1;
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if(Final->GetTraj(MR,rotation,timespan)) WTnode_gettranslation(MobileR,test); WTnode_getorientation(MobileR,viewrot); WTnode_settranslation(MobileR,MR);
WTnode_axisrotation(MobileR,Y,(float)rotation, WTFRAME_LOCAL);
pos[0]=MR[0]; pos[1]=-100.0f; pos[2]=MR[2]; WTviewpoint_setposition(camera,pos); WTviewpoint_setorientation(camera,viewrot); break; ; switch(tolower(key)) case 'q': WTuniverse_stop(); break; case WTKEY_F1:
WTwindow_setprojection(MainWin, WTPROJECTION_SYMMETRIC);
pos[0]=-750.0f; pos[1]=-100.0f; pos[2]=300.0f; WTviewpoint_setposition(camera1,pos); WTwindow_setviewpoint(MainWin,camera1); break; case WTKEY_F2: posTop[0]=-748.0f; posTop[1]=-904.0f; posTop[2]=617.0f; WTviewpoint_setposition(TopView,posTop);
WTwindow_setprojection(MainWin, WTPROJECTION_ORTHOGRAPHIC);
WTwindow_zoomviewpoint(MainWin); WTwindow_setviewpoint(MainWin,TopView); break; case WTKEY_F3: camera=WTviewpoint_new();
WTwindow_setprojection(MainWin, WTPROJECTION_SYMMETRIC);
WTviewpoint_setposition(camera,pos); WTviewpoint_setorientation(camera,viewrot); WTwindow_setviewpoint(MainWin,camera); break; case WTKEY_END: Top=WTwindow_new(0,0,415,374,WTWINDOW_DEFAULT|
WTWINDOW_NOBORDER); WTwindow_setviewpoint(Top,TopView); WTwindow_setprojection(Top,
WTPROJECTION_ORTHOGRAPHIC); WTwindow_zoomviewpoint(Top); posTop[0]=62.0f; posTop[1]=-1000.0f; posTop[2]=-178.0f; WTviewpoint_setposition(TopView,posTop); con=1; break; case WTKEY_LEFTARROW: posTop[0]=posTop[0]+1; WTviewpoint_setposition(TopView,posTop); break; case WTKEY_RIGHTARROW: posTop[0]=posTop[0]-1; WTviewpoint_setposition(TopView,posTop); break; case WTKEY_DOWNARROW: posTop[2]=posTop[2]+1; WTviewpoint_setposition(TopView,posTop);
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break; case WTKEY_UPARROW: posTop[2]=posTop[2]-1; WTviewpoint_setposition(TopView,posTop); break; ; void Path_Planning(int *CMap) int xi=0, xg=0, yi=0, yg=0, meetxi=0, meetyi=0, meetxg=0, meetyg=0; unsigned int counter=0; unsigned int steps=0; Astar *astarsearch=new Astar; //Obtaining Path Searching Information cout<<"The coordinate for initial point\n"<<endl; cout<<"Initial x: "; cin>>meetxi; cout<<"Initial y: "; cin>>meetyi; //Create Goal Node cout<<"\nThe coordinate for goal point\n"<<endl; cout<<"Goal x: "; cin>>meetxg; cout<<"Goal y: "; cin>>meetyg; xi=meetxi/7.5; xg=meetxg/7.5; yi=meetyi/7.5; yg=meetyg/7.5; //C-Space Generation astarsearch->Mapping(xi,yi,xg,yg,CMap); //Set Start and Goal States in Astar Search Algorithm State SearchState=SEARCH_STATE_SEARCHING; unsigned int SearchLoop=0; astarsearch->SetStartAndGoalState(xi,xg,yi,yg); //Start with the Graph Searching do SearchState=astarsearch->SearchRule(); SearchLoop++; while(SearchState == SEARCH_STATE_SEARCHING); //Start of the solution path extraction if(SearchState == SEARCH_STATE_SUCCEEDED) Astar::SearchNodeProperty *SolvedPath = astarsearch
->GetSolutionStart(); if(!SolvedPath) exit(0); ;
//Adding Solved Path into Another Object Final->AddSolvedNode(SolvedPath->x, SolvedPath->y, steps); SolvedPath->NodeInfo(); for(;;) SolvedPath=astarsearch->GetSolutionNext();
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if(!SolvedPath) break; steps++; Final->AddSolvedNode(SolvedPath->x, SolvedPath->y, steps); SolvedPath->NodeInfo(); ; cout<<"Solution steps: "<<steps<<endl; else if(SearchState == SEARCH_STATE_FAILED) cout<<"Search terminated -> Goal state failed to be found\n"<<endl;
exit(0); ; cout<<"Vertices Visited: "<<SearchLoop<<endl; //Path Refining to Remove ‘cusps’ Final->Repath(astarsearch); //The Generation of Time-based Trajectory from Geometrical Path Final->Trajectory(); //Delete the Object for Path Planning to Free Up the Memory delete astarsearch; ;
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Appendix C
Program Modules for the Experimental Mobile Manipulator
The most important three program modules in the program, i.e., main(),
ReadMobileManipulatorSensors(), and MobileManipulator_RAC_KBFAFC_RUN() are shown in Figures C.1, C.2 and C.3 respectively.
Figure C.1: Program module main().
As can be seen in Figure C.1, the first routine executed in the program is SystemCalibration()
followed by the initializations. The RACAFC and RACKBFAFC schemes are executed consecutively. A routine of MobileManipulatorREMOTE() was added to the end of program to allow user to control (move) the robot manually by remote system using the keyboard of PC. This is important for adjusting the initial (angle) position of the arm when the system starts to be executed.
int main(void) clrscr; printf("\n\n \n"); printf(" Welcome to RTM MobileManipulator Online System\n"); printf(" Version 1.852 (c)2005 by Endra Pitowarno\n\n"); printf(" Please wait for a moment\n"); printf(" The system is being calibrated\n\n"); SystemCalibration(); Display_Init(); Motor_Init(); MMotor_Init(); MobileManipulator_RAC_AFC_RUN(); MobileManipulator_RAC_KBFAFC_RUN(); MobileManipulatorREMOTE(); CloseOperation(); return 0;
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float ReadMobileManipulatorSensors() Link1_DIR = COM_DIR & 0x01; Link2_DIR = COM_DIR & 0x02; LinkL_DIR = MCOM_DIR & KeepML; LinkR_DIR = MCOM_DIR & KeepMR; if (LinkL_DIR == ML_reverse) th_d_L_act = -(MRead_ADC2()-cal_MADC2)*ML_th_d_Calib; gettime(&t); tsequel_L_rev = t.ti_min*60. + t.ti_sec+t.ti_hund/100.-subtt; th_L_act = th_L_act - fabs(th_d_L_act*(tsequel_L_rev-tsequel_L_rev_OLD)); th_dd_L_act = -(MRead_ADC4()*1.-cal_MADC4)/20480.; Ic_L = -(fabs(MRead_ADC6()*1.-cal_MADC6))/2048.*50.; if (LinkL_DIR == ML_forward) th_d_L_act = (MRead_ADC2()-cal_MADC2)*ML_th_d_Calib; gettime(&t); tsequel_L_for = t.ti_min*60. + t.ti_sec+t.ti_hund/100.-subtt; th_L_act = th_L_act + th_d_L_act*(tsequel_L_for-tsequel_L_for_OLD); th_dd_L_act = (MRead_ADC4()*1.-cal_MADC4)/20480.; Ic_L = fabs(MRead_ADC6()*1.-cal_MADC6)/2048.*50.; if (LinkR_DIR == MR_forward) th_d_R_act = (MRead_ADC1()-cal_MADC1)*MR_th_d_Calib; gettime(&t); tsequel_R_for = t.ti_min*60. + t.ti_sec+t.ti_hund/100.-subtt; th_R_act = th_R_act + th_d_R_act*(tsequel_R_for-tsequel_R_for_OLD); th_dd_R_act = (MRead_ADC3()*1.-cal_MADC3)/20480.; Ic_R = fabs(MRead_ADC5()*1.-cal_MADC5)/2048.*50.; if (LinkR_DIR == MR_reverse) th_d_R_act = -(MRead_ADC1()-cal_MADC1)*MR_th_d_Calib; gettime(&t); tsequel_R_rev = t.ti_min*60. + t.ti_sec+t.ti_hund/100.-subtt; th_R_act = th_R_act - fabs(th_d_R_act*(tsequel_R_rev-tsequel_R_rev_OLD)); th_dd_R_act = -(MRead_ADC3()*1.-cal_MADC3)/20480.; Ic_R = -(fabs(MRead_ADC5()*1.-cal_MADC5))/2048.*50.; tsequel_L_rev_OLD = tsequel_L_rev; tsequel_L_for_OLD = tsequel_L_for; tsequel_R_rev_OLD = tsequel_R_rev; tsequel_R_for_OLD = tsequel_R_for;
<page 1 of 2 of Figure C.2> continued...
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Figure C.2: Program module ReadMobileManipulatorSensors().
PHI_d_act = -rWheel/(2.*halfB)*th_d_L_act+rWheel/(2.*halfB)*th_d_R_act; PHI_act = PHI_act + PHI_d_act*(tt-tsequel_PHI_OLD); tsequel_PHI_OLD = tt; XB_d_act = th_d_L_act*(rWheel/2.*cos(PHI_act)+dGtoF*rWheel/(2.*halfB)*sin(PHI_act)) + th_d_R_act*(rWheel/2.*cos(PHI_act)-dGtoF*rWheel/(2.*halfB)*sin(PHI_act)); YB_d_act = th_d_L_act*(rWheel/2.*sin(PHI_act)-dGtoF*rWheel/(2.*halfB)*cos(PHI_act)) + th_d_R_act*(rWheel/2.*sin(PHI_act)+ dGtoF*rWheel/(2.*halfB)*cos(PHI_act)); XB_act = XB_act + XB_d_act*(tt-tsequel_XYB_act_OLD); YB_act = YB_act + YB_d_act*(tt-tsequel_XYB_act_OLD); tsequel_XYB_act_OLD = tt; /***************************************** Manipulator's Sensors ***/ th_1_act = ReadEncoderSATU()/4096.*2*PI; th_2_act = ReadEncoderDUA()/4096.*2*PI; if (Link1_DIR == M1_CW) th_d_1_act = -(fabs(Read_ADC3()*1.-cal_ADC3*1.)*th_d_1_calib); th_dd_1_act = fabs(Read_ADC5()*1.-cal_ADC5*1.)/2048.*cal_thdd1; Ic_1 = Sample_Ic_1/200.; if (Link1_DIR == M1_CCW) th_d_1_act = fabs(Read_ADC3()*1.-cal_ADC3*1.)*th_d_1_calib; th_dd_1_act = -(fabs(Read_ADC5()*1.-cal_ADC5*1.))/2048.*cal_thdd1; Ic_1 = Sample_Ic_1/200.; if (Link2_DIR == M2_CW) th_d_2_act = -(fabs(Read_ADC4()*1.-cal_ADC4*1.)*th_d_2_calib); th_dd_2_act = fabs(Read_ADC6()*1.-cal_ADC6*1.)/2048.*cal_thdd2; Ic_2 = Sample_Ic_2/400.; if (Link2_DIR == M2_CCW) th_d_2_act = fabs(Read_ADC4()*1.-cal_ADC4*1.)*th_d_2_calib; th_dd_2_act = -(fabs(Read_ADC6()*1.-cal_ADC6*1.))/2048.*cal_thdd2; Ic_2 = Sample_Ic_2/400.; /************************************************************/ return(th_R_act,th_L_act, th_1_act,th_2_act, th_d_R_act,th_d_L_act, th_d_1_act,th_d_2_act, th_dd_R_act,th_dd_L_act, th_dd_1_act,th_dd_2_act, Ic_1,Ic_2,Ic_L,Ic_R, PHI_act,PHI_d_act, XB_act,YB_act,XB_d_act,YB_d_act); <page 2 of 2 of Figure C.2>
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In Figure C.2, it can be seen that the sign of sensors value of velocity and acceleration is obtained by combining the direction of motor’s moving according to the sensors value. If the direction is clock-wise (CW), then the sensor value is converted to negative vice versa.
/************* Integrated MOBILE MANIPULATOR SECTION (RAC-KBFAFC) ****/ int MobileManipulator_RAC_KBFAFC_RUN() i = 0; ii = 0; th_R_des = 0; th_L_des = 0; PHI_des_tt = 0; tsequel_th_RL_des_OLD = 0; PHI_act = 0; XB_act = 0; YB_act = 0; TEc = 0; tt = 0; th_L_act = 0; th_R_act = 0; data_t_Rec = fopen("d:/endra/kt_MM.dat","w+"); data_TE_Arm_Rec = fopen("d:/endra/kTE_Arm.dat","w+"); data_TE_Body_Rec = fopen("d:/endra/kTE_Body.dat","w+"); data_X_des_Rec = fopen("d:/endra/kX_des.dat","w+"); data_Y_des_Rec = fopen("d:/endra/kY_des.dat","w+"); data_XB_des_Rec = fopen("d:/endra/kXB_des.dat","w+"); data_YB_des_Rec = fopen("d:/endra/kYB_des.dat","w+"); data_X_act_Rec = fopen("d:/endra/kX_act.dat","w+"); data_Y_act_Rec = fopen("d:/endra/kY_act.dat","w+"); data_XB_act_Rec = fopen("d:/endra/kXB_act.dat","w+"); data_YB_act_Rec = fopen("d:/endra/kYB_act.dat","w+"); data_th_dd_1_act_Rec = fopen("d:/endra/kth_dd_1_act.dat","w+"); data_th_dd_2_act_Rec = fopen("d:/endra/kth_dd_2_act.dat","w+"); data_Ic_1_Rec = fopen("d:/endra/kIc_1.dat","w+"); data_Ic_2_Rec = fopen("d:/endra/kIc_2.dat","w+"); Display_Sys_MM(); Display_ProgramCode(); RAFCON_LOGO_RACKBFAFC(); SetControlParametersMM(); Set_Intelligent_KBF_Parameter(); MobileManipulatorREMOTE(); ManipulatorHomePosition(); MobileManipulatorREMOTE(); MessagesBOTTOM_Ready(); MessagesBOTTOM_RUN(); PHI_d_des = -rWheel/(2.*halfB)*th_d_L_des+rWheel/(2.*halfB)*th_d_R_des; PHI_act = InitialOrientationPHI; SetTimeRUN(); GetCurrentTime(); for(;;) gettime(&t); tt = t.ti_min*60. + t.ti_sec+t.ti_hund/100.-subtt; ReadMobileManipulatorSensors(); RealTimeDisplay(); Tq1 = Ic_1*Ktn1; Tq2 = Ic_2*Ktn2; KVkbf1 = KBF_module_1(); KVkbf2 = KBF_module_2(); ActionKBFAFC1 = (Tq1-th_dd_1_act*KVkbf1) / Ktn1; ActionKBFAFC2 = (Tq2-th_dd_2_act* KVkbf2) / Ktn2; <page 1 of 4 of Figure C.3> continued...
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/***************************** Manipulator RUN Section ************************/ if (th_1_act > th_1_des) Status_DIR = COM_DIR & KeepM2; COM_DIR = (Status_DIR + M1_CW); outp(DIG_OUT_Address,COM_DIR); ActionR = (fabs( Kp1*(th_1_des-th_1_act) + Kd1*(th_d_1_des-th_d_1_act))*(AFCCA_Value1+KVkbf1)/Ktn1 + ActionKBFAFC1)*Ktn1*Kgearbox1+M1_Calib; if(ActionR>=4000) ActionR=4000; ActionH = (ActionR/16); ActionL = (ActionR-floor(ActionH*16)); outp(DAC_Motor1_H,ActionH); outp(DAC_Motor1_L,ActionL); if (th_1_act < th_1_des ) Status_DIR = COM_DIR & KeepM2; COM_DIR = (Status_DIR + M1_CCW); outp(DIG_OUT_Address,COM_DIR); ActionR = (fabs( Kp1*(th_1_des-th_1_act) + Kd1*(th_d_1_des-th_d_1_act))*(AFCCA_Value1+KVkbf1)/Ktn1 + ActionKBFAFC1)*Ktn1*Kgearbox1+M1_Calib; if(ActionR>=4000) ActionR=4000; ActionH = ActionR/16; ActionL = ActionR-floor(ActionH*16); outp(DAC_Motor1_H,ActionH); outp(DAC_Motor1_L,ActionL); outp(PPIPA,ActionH); if (th_2_act > th_2_des) Status_DIR = COM_DIR & KeepM1; COM_DIR = (Status_DIR + M2_CW); outp(DIG_OUT_Address,COM_DIR); ActionR = (fabs( Kp2*(th_2_des-th_2_act) + Kd2*(th_d_2_des-th_d_2_act))*(AFCCA_Value2+KVkbf2)/Ktn2 + ActionKBFAFC2)*Ktn2*Kgearbox2+M2_Calib; if(ActionR>=4000) ActionR=4000; ActionH = ActionR/16; ActionL = ActionR-floor(ActionH*16); outp(DAC_Motor2_H,ActionH); outp(DAC_Motor2_L,ActionL); if (th_2_act < th_2_des ) Status_DIR = COM_DIR & KeepM1; COM_DIR = (Status_DIR + M2_CCW); outp(DIG_OUT_Address,COM_DIR); ActionR = (fabs( Kp2*(th_2_des-th_2_act) + Kd2*(th_d_2_des-th_d_2_act))*(AFCCA_Value2+KVkbf2)/Ktn2 + ActionKBFAFC2)*Ktn2*Kgearbox2+M2_Calib; if(ActionR>=4000) ActionR=4000; ActionH = ActionR/16; ActionL = ActionR-floor(ActionH*16); outp(DAC_Motor2_H,ActionH); outp(DAC_Motor2_L,ActionL); /************************ Mobile Platform RUN Section *************************/ if (th_L_act > th_L_des) MStatus_DIR = MCOM_DIR & KeepMR; MCOM_DIR = (MStatus_DIR + ML_reverse); outp(MDIG_OUT_Address,MCOM_DIR); MActionR = fabs( KpL*(th_L_des-th_L_act) + KdL*(th_d_L_des-th_d_L_act)) *KtnL*KgearboxL+ML_Calib; if(MActionR>=4000) MActionR=4000; MActionH = MActionR/16; MActionL = (MActionR-floor(MActionH*16)); outp(MDAC2_MotorL_H,MActionH); outp(MDAC2_MotorL_L,MActionL); <page 2 of 4 of Figure C3> continued...
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if (th_L_act < th_L_des ) MStatus_DIR = MCOM_DIR & KeepMR; MCOM_DIR = (MStatus_DIR + ML_forward); outp(MDIG_OUT_Address,MCOM_DIR); MActionR = fabs( KpL*(th_L_des-th_L_act) + KdL*(th_d_L_des-th_d_L_act)) *KtnL*KgearboxL+ML_Calib; if(MActionR>=4000) MActionR=4000; MActionH = MActionR/16; MActionL = MActionR-floor(MActionH*16); outp(MDAC2_MotorL_H,MActionH); outp(MDAC2_MotorL_L,MActionL); outp(MPPIPA,MActionH); if (th_R_act > th_R_des) MStatus_DIR = MCOM_DIR & KeepML; MCOM_DIR = (MStatus_DIR + MR_reverse); outp(MDIG_OUT_Address,MCOM_DIR); MActionR = fabs( KpR*(th_R_des-th_R_act) + KdR*(th_d_R_des-th_d_R_act)) *KtnR*KgearboxR+MR_Calib; if(MActionR>=4000) MActionR=4000; MActionH = MActionR/16; MActionL = MActionR-floor(MActionH*16); outp(MDAC1_MotorR_H,MActionH); outp(MDAC1_MotorR_L,MActionL); if (th_R_act < th_R_des ) MStatus_DIR = MCOM_DIR & KeepML; MCOM_DIR = (MStatus_DIR + MR_forward); outp(MDIG_OUT_Address,MCOM_DIR); MActionR = fabs( KpR*(th_R_des-th_R_act) + KdR*(th_d_R_des-th_d_R_act)) *KtnR*KgearboxR+MR_Calib; if(MActionR>=4000) MActionR=4000; MActionH = MActionR/16; MActionL = MActionR-floor(MActionH*16); outp(MDAC1_MotorR_H,MActionH); outp(MDAC1_MotorR_L,MActionL); if (tt >= Tstop) outp(DAC_Motor1_H,0x00); outp(DAC_Motor1_L,0x00); outp(DAC_Motor2_H,0x00); outp(DAC_Motor2_L,0x00); outp(MDAC1_MotorR_H,0x00); outp(MDAC1_MotorR_L,0x00); outp(MDAC2_MotorL_H,0x00); outp(MDAC2_MotorL_L,0x00); int j = ii; for (i=0; i<j; i++) fprintf(data_t_Rec, "%10f \n",t_Rec[i]); fprintf(data_TE_Arm_Rec, "%10f \n",TE_Arm_Rec[i]); fprintf(data_TE_Body_Rec, "%10f \n",TE_Body_Rec[i]); fprintf(data_X_des_Rec, "%10f \n",X_des_Rec[i]); fprintf(data_Y_des_Rec, "%10f \n",Y_des_Rec[i]); fprintf(data_XB_des_Rec, "%10f \n",XB_des_Rec[i]); fprintf(data_YB_des_Rec, "%10f \n",YB_des_Rec[i]); fprintf(data_X_act_Rec, "%10f \n",X_act_Rec[i]); fprintf(data_Y_act_Rec, "%10f \n",Y_act_Rec[i]); fprintf(data_XB_act_Rec, "%10f \n",XB_act_Rec[i]); fprintf(data_YB_act_Rec, "%10f \n",YB_act_Rec[i]); fprintf(data_th_dd_1_act_Rec, "%10f \n",th_dd_1_act_Rec[i]); fprintf(data_th_dd_2_act_Rec, "%10f \n",th_dd_2_act_Rec[i]); fprintf(data_Ic_1_Rec, "%10f \n",Ic_1_Rec[i]); fprintf(data_Ic_2_Rec, "%10f \n",Ic_2_Rec[i]); <page 3 of 4 of Figure C3> continued...
181
Figure C.3: Program module MobileManipulator_RAC_KBFAFC_RUN().
The program module MobileManipulator_RAC_KBFAFC_RUN() as shown in Figure C.3
contains three main parts that are manipulator control loop, mobile platform control loop, and Data Recording/Saving routines. Note that in this program, the RACKBFAFC scheme was applied to the manipulator section only, while RACAFC was applied to the platform. An emergency STOP facility was implemented at the end of the program as a safety precautionary measure. Users can immediately stop the program execution if a fault operation occurs by hitting any key of the keyboard when the robot is running.
fclose(data_YB_des_Rec); fclose(data_X_act_Rec); fclose(data_Y_act_Rec); fclose(data_t_Rec); fclose(data_TE_Arm_Rec); fclose(data_TE_Body_Rec); fclose(data_X_des_Rec); fclose(data_Y_des_Rec); fclose(data_XB_des_Rec); fclose(data_XB_act_Rec); fclose(data_YB_act_Rec); fclose(data_th_dd_1_act_Rec); fclose(data_th_dd_2_act_Rec); fclose(data_Ic_1_Rec); fclose(data_Ic_2_Rec); setviewport(x/2+8,308,x/2+285,320,CLIP_ON); clearviewport(); sprintf(msg," RACKBFAFC : Check the Results !",10); outtextxy(0,2,msg); getch(); return 0; jj=jj+1; if(jj>=4) tt_old = tt; t_Rec[ii] = tt; TE_Arm_Rec[ii] = TErA; TE_Body_Rec[ii] = TEr; X_des_Rec[ii] = XdesV; Y_des_Rec[ii] = YdesV; XB_des_Rec[ii] = XB_des; YB_des_Rec[ii] = YB_des; X_act_Rec[ii] = XactV; Y_act_Rec[ii] = YactV; XB_act_Rec[ii] = XB_act; YB_act_Rec[ii] = YB_act; th_dd_1_act_Rec[ii] = th_dd_1_act; th_dd_2_act_Rec[ii] = th_dd_2_act; Ic_1_Rec[ii] = Ic_1; Ic_2_Rec[ii] = Ic_2; ii++; jj=0; /*************************** emergency STOP *****************************/ while(kbhit()) VR = MRead_ADC7(); if(VR < 2990) sound(1200); VL = MRead_ADC8(); if(VL < 2990) sound(800); outp(DAC_Motor1_H,0x00); outp(DAC_Motor1_L,0x00); outp(DAC_Motor2_H,0x00); outp(DAC_Motor2_L,0x00); outp(MDAC1_MotorR_H,0x00); outp(MDAC1_MotorR_L,0x00); outp(MDAC2_MotorL_H,0x00); outp(MDAC2_MotorL_L,0x00); getch(); nosound(); return 0; <page 4 of 4 of Figure C.3>
182
Appendix D
List of Publications
1. Tang, H. H., Mailah, M. and Kasim, M. ‘Stabilization of Nonholonomic Wheeled
Mobile Robot through Intelligent Active Force Control’. Proceedings of
Advanced Technology Congress – Intelligent Systems and Robotics (CISAR
2003). May 20-21, 2003. Kuala Lumpur, Malaysia: Institute of Advanced
Technology, UPM. 2003.
2. Tang, H. H., Mailah, M. and Kasim, M. Collision-Free Global Path Planning for
a Holonomic Mobile Robot in a Known Stationary Virtual Environment.
Proceedings of Malaysian Science and Technology (MSTC) – Information and
Communication Technology. September 23-25, 2003. Kuala Lumpur, Malaysia:
MSTC. 2003. 328-335.
3. Didik Setyo Purnomo and Musa Mailah, ‘Trajectory Tracking of Nonholonomic
Mobile Robot Using Intelligent Active Force Control’, Procs. of Advanced
Technology Congress 2003, Marriot Hotel, Kuala Lumpur, May 2003.
4. Didik Setyo Purnomo and Musa Mailah, ‘Control of Nonholonomic Mobile
Robot Using Adaptive Active Force Control Strategy’, Procs. of CARS-FOF
2003, SIRIM, Kuala Lumpur, July 2003.
5. Didik S.P., Musa Mailah, ‘Optimization of The Membership Function in A Fuzzy
Logic Based Active Force Control Applied To A Wheeled Mobile Robot’, Procs.
of MSTC2003, Hotel Cititel, Kuala Lumpur, 23-26 September 2003.
6. Endra Pitowarno, Musa Mailah, ‘A Disturbance Cancellation Method Of A
Differentially Driven Non-Holonomic Mobile Robot Using Active Force Control
with Optimized Crude Approximation’, Procs. of MSTC2003, Hotel Cititel,
Kuala Lumpur, 23-26 September 2003.
183
7. Endra Pitowarno, Musa Mailah, ‘A Robust Motion Control of A Differentially
Driven Mobile Robot Using Resolved Acceleration and Active Force Control’,
Procs. of IES 2003, December 16, 2003, Surabaya, Indonesia.
8. Endra Pitowarno, Musa Mailah, Hishamuddin Jamaluddin ‘Motion Control of
Mobile Robot Using Resolved Acceleration and Active Force Control’, Paper No.
128, ICCC 2004, 25-28 May 2004, Zakopane, Poland.
9. Didik Setyo Purnomo, Endra Pitowarno, Musa Mailah, ‘Motion Control of A
Nonholonomic Mobile Robot Using Fuzzy Logic Active Force Control’, Procs.
of IES 2004, October 2004, Surabaya, Indonesia.
10. Endra Pitowarno, Musa Mailah, Hishamuddin Jamaluddin, ‘Motion Control of
Mobile Manipulator Using Resolved Acceleration and Iterative Learning Active
Force Control’, Procs. of ICOM05, KL, May 2005.
11. Endra Pitowarno, Musa Mailah, ‘Resolved Acceleration and Knowledge Based
Fuzzy Active Force Control for Mobile Manipulator’, Procs. of ROVISP05, USM
Penang, July 2005.
12. Musa Mailah, Endra Pitowarno, Hishamuddin Jamaluddin, ‘Robust Motion
Control for Mobile Manipulator Using Resolved Acceleration and Proportional-
Integral Active Force Control’, International Journal of Advanced Robotic
Systems, June 2005, Vol. 2, No.2, pp 125-134.
13. Tang Howe Hing, Musa Mailah and M.K. Abdul Jalil, ‘Robust Intelligent Active
Force Control of Nonholonomic Wheeled Mobile Robot’, Jurnal Teknologi (D),
UTM, June 2006.
14. Musa Mailah, Tang Howe Hing, M Kasim A. Jalil, ‘Virtual Wheeled Mobile
Robot Simulator with Integrated Motion Planning and Active Force Control’ in
Advanced Technologies, Research – Development – Application, Ed. Bojan Lalic,
Pro Literatur Verlag, Germany, ISBN 3-86611-197-5, September 2006, pp. 615-
640.
15. Tang Howe Hing, Musa Mailah, ‘Motion Control of Nonholonomic Wheeled
Mobile Robot in A Structured Layout’, Jurnal Mekanikal, June 2006.
184
16. Tang Howe Hing, Musa Mailah, M.K. Abdul Jalil ‘Virtual Simulator for Control
of Autonomous Nonholonomic Wheeled Mobile Robot’, submitted to Brazilian
Journal of Mechanical Science & Engineering, August 2006.
185
Appendix E
Achievements / Outputs / Beneficiaries / Awards
A. BOOK CHAPTER:
1. Musa Mailah, Tang Howe Hing, M Kasim A. Jalil, ‘Virtual Wheeled Mobile Robot Simulator with Integrated Motion Planning and Active Force Control’ in Advanced Technologies, Research – Development – Application, Ed. Bojan Lalic, Pro Literatur Verlag, Germany, ISBN 3-86611-197-5, September 2006, pp. 615-640.
B. INTERNATIONAL JOURNAL:
1. Musa Mailah, Endra Pitowarno, Hishamuddin Jamaluddin, ‘Robust Motion Control for Mobile Manipulator Using Resolved Acceleration and Proportional-Integral Active Force Control’, International Journal of Advanced Robotic Systems, June 2005, Vol. 2, No.2, pp 125-134.
2. Tang Howe Hing, Musa Mailah, M.K. Abdul Jalil ‘Virtual Simulator for Control of Autonomous Nonholonomic Wheeled Mobile Robot’, submitted to Brazilian Journal of Mechanical Science & Engineering, August 2006.
C. NATIONAL JOURNAL:
1. Tang Howe Hing, Musa Mailah and M.K. Abdul Jalil, ‘Robust Intelligent Active Force Control of Nonholonomic Wheeled Mobile Robot’, Jurnal Teknologi (D), UTM, June 2006.
2. Tang Howe Hing, Musa Mailah, ‘Motion Control of Nonholonomic Wheeled Mobile Robot in A Structured Layout’, Jurnal Mekanikal, June 2006.
D. INTERNATIONAL CONFERENCE:
1. Tang, H. H., Mailah, M. and Kasim, M. ‘Stabilization of Nonholonomic Wheeled Mobile Robot through Intelligent Active Force Control’. Proceedings of Advanced Technology Congress – Intelligent Systems and Robotics (CISAR 2003). May 20-21, 2003. Kuala Lumpur, Malaysia: Institute of Advanced Technology, UPM. 2003.
2. Didik Setyo Purnomo and Musa Mailah, ‘Trajectory Tracking of Nonholonomic Mobile Robot Using Intelligent Active Force Control’, Procs. of Advanced Technology Congress 2003, Marriot Hotel, Kuala Lumpur, May 2003.
186
3. Didik Setyo Purnomo and Musa Mailah, ‘Control of Nonholonomic Mobile Robot Using Adaptive Active Force Control Strategy’, Procs. of CARS-FOF 2003, SIRIM, Kuala Lumpur, July 2003.
4. Endra Pitowarno, Musa Mailah, ‘A Robust Motion Control of A Differentially Driven Mobile Robot Using Resolved Acceleration and Active Force Control’, Procs. of IES 2003, December 16, 2003, Surabaya, Indonesia.
5. Endra Pitowarno, Musa Mailah, Hishamuddin Jamaluddin ‘Motion Control of Mobile Robot Using Resolved Acceleration and Active Force Control’, Paper No. 128, ICCC 2004, 25-28 May 2004, Zakopane, Poland.
6. Didik Setyo Purnomo, Endra Pitowarno, Musa Mailah, ‘Motion Control of A Nonholonomic Mobile Robot Using Fuzzy Logic Active Force Control’, Procs. of IES 2004, October 2004, Surabaya, Indonesia.
7. Endra Pitowarno, Musa Mailah, Hishamuddin Jamaluddin, ‘Motion Control of Mobile Manipulator Using Resolved Acceleration and Iterative Learning Active Force Control’, Procs. of ICOM05, KL, May 2005.
8. Endra Pitowarno, Musa Mailah, ‘Resolved Acceleration and Knowledge Based Fuzzy Active Force Control for Mobile Manipulator’, Procs. of ROVISP05, USM Penang, July 2005.
E. NATIONAL CONFERENCE:
1. Endra Pitowarno, Musa Mailah, ‘A Disturbance Cancellation Method Of A Differentially Driven Non-Holonomic Mobile Robot Using Active Force Control with Optimized Crude Approximation’, Procs. of MSTC2003, Hotel Cititel, Kuala Lumpur, 23-26 September 2003.
2. Tang, H. H., Mailah, M. and Kasim, M. Collision-Free Global Path Planning for a Holonomic Mobile Robot in a Known Stationary Virtual Environment. Proceedings of Malaysian Science and Technology (MSTC) – Information and Communication Technology. September 23-25, 2003. Kuala Lumpur, Malaysia: MSTC. 2003. 328-335.
3. Didik S.P., Musa Mailah, ‘Optimization of The Membership Function in A Fuzzy Logic Based Active Force Control Applied To A Wheeled Mobile Robot’, Procs. of MSTC2003, Hotel Cititel, Kuala Lumpur, 23-26 September 2003.
F. PHD STUDENT:
1. Endra Pitowarno, Intelligent Active Force Control of A Mobile Manipulator, November 2002-February 2006 (Completed).
G. MENG STUDENT: 1. Tang Howe Hing, Implementation of Motion Planning and Active Force Control
to A Virtual Wheeled Mobile Robot, May 2002-July 2004 (Completed). 2. Didik Setyo Purnomo, Design and Development of Intelligent Mobile Robot
Using Active Force Control, May 2002-December 2004 (Completed).
187
H. AWARD:
1. A Bronze Medal in Exposition Science, Technology and Innovation (ST&I 2004) for the project research, ‘Autonomous Wheeled Mobile Manipulator Using Active Force Control’, 27-29 August 2004, Kuala Lumpur.
I. COLLABORATION:
• Collaboration with Polis Di Raja Malaysia (PDRM) on Retrofit of Mobile Bomb Disposal Robot, 2005-2006.
• A loaned and initially malfunctioned Cyclops Mobile Robot (a mobile bomb disposal unit) has been successfully retrofitted with the aid of five (5) PSM students and an Assistant Research Officer in 2006.
188
Appendix F
Mechanical Design and Production Drawings of Mobile
Manipulator
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